Diahann Carroll says that she has always loved to over-think an outfit, to analyse what she wears to an exacting degree. When auditioning for the 1968 TV show Julia, for instance - the first US sitcom ever to centre on a black woman - Carroll decided to wear an ordinary-looking shift, which was actually by Givenchy. She landed the part. And in honour of this instinct, I over-think the outfit that I wear to meet her: a simple, well-cut Ghost dress, which I hope we'll bond over. She does notice the dress. The bonding takes longer.

We meet in her gorgeous apartment in Los Angeles in a building that seems to be diva towers (Joan Collins has an apartment in the same block). Carroll looks gorgeous too, but when I compliment her, she seems cross. "Come off it, I'm 73." This combative spirit is reflected in her new autobiography, The Legs Are The Last To Go, in which she comes across as a bruised but feisty character. "Yes, I'm ambitious," she writes, "a rampant careerist who is as dedicated and vain as any performer in the business. I don't know if that will ever change."

Her ambition has stood her in good stead. Carroll was born in Harlem in 1935 to hard-working parents who doted on her, and by the age of 17 she was performing as a singer at the Latin Quarter nightclub in New York. This was an era when black actors were all too regularly cast as maids, or not at all, but Carroll was one of a brilliant vanguard who broke through. At 19 she was cast opposite Dorothy Dandridge in the film Carmen Jones, and then Truman Capote put his faith in her to play the ingénue in the Broadway musical based on his novella House of Flowers. Richard Rodgers wrote the musical No Strings for her; when she won the Tony for best actress for the show in 1962, she was the first black woman ever to be given the award. She was nominated for an Oscar in 1974 for the movie Claudine, and in the 1980s Aaron Spelling cast her as Dominique Deveraux in Dynasty. "The first black bitch on television," Carroll says happily.

She seems to warm to confrontation far more than compliments, and her life has been full of it. Singing in a casino in Lake Tahoe at the start of her career, the band leader stood in front of her to block her from the audience. How terrible did she feel, I ask, when he said, "No one wants to see you because you're black?" She rises stiffly in her chair. "No, what he actually said was, 'No one here wants to hear a nigger sing'. It's adorable that people like you don't want to say the nigger word. What do you feel when you hear [the words] 'white trash'?" Her eyes flash and I don't respond.

"I said that because I thought it wasn't kind and I wanted to see how you would react. And you did react by not reacting ... What you're saying is you don't deal with it because it's not necessary for you to deal with it, so why is it necessary for me to deal with that word?"

She grew up aware of the paper bag test - if you were browner than a brown paper bag you weren't allowed into certain social clubs - and she says she doesn't believe that being colour blind exists. "Denying that I'm a black woman does me no service." When I tell her I was shocked to read about the amount of racism she suffered in the 1950s, she gives me a cold stare. "In my profession we have made some strides, but not many," she says. "There are not enough black actors making $20m a picture. It is not representative."

Carroll was brought up in an era in which female sexuality was supposed to stay hidden and if you had a relationship with someone you had to marry them. "I very much encourage women not to do that," she says drolly. She has been married four times in all. Her first husband was Monty Kay, with whom she had a daughter; her second was Freddie Glusman, who was abusive; she then married academic Robert DeLeon, who spent too much of her money, before dying in a car crash; last came a union with singer Vic Damone, who loved golf more than life with her, and who she divorced in the 1990s. Isn't it strange that the strongest, most feminist women always attract the most diabolical men? "I know," she says sadly, before thanking me for calling her a feminist. She notes that a successful career is not usually the perfect accompaniment to a good marriage, "unless a man wants to be Mr Mom, and I don't think that would have worked for me," she laughs.

She thinks that perhaps only the marriage to her first husband was a sensible decision, but he came along when she was too young. While with him, she met Sidney Poitier on the set of Porgy and Bess, and there was an impossible attraction. She tried to keep away - he was married too - but their affair continued on and off for nine years. "In the long run it didn't work," says Carroll. "He was a wonderful and giving actor. We worked together in Paris Blues and I auditioned for A Raisin in the Sun but I did not get it and I am glad, because we were at the height of everything in our personal lives and it would have been awful."

Carroll's daughter, Suzanne, is her only child, and she admits that she was never in the running for mother of the year. "The bond was there early with my daughter, but also anger about the fact I was not there more often. I think mothers and daughters are always competitive and after a certain age there should not be two women under the same roof." Her daughter hates to be mentioned in interviews, to the extent that Carroll won't even say whereabouts in Europe she now lives.

Would she have liked more children? "I lost two children [to miscarriage]. That's why when we talk about racism it will always take third, fourth, fifth place to some of the other things that have happened to me that are much more meaningful than being in a room with an idiot who is going to judge the colour of my skin. I wish I had more children, I really do. I wanted babies so badly. I lost my first two babies and it was horrible."

All her confrontation melts away when she talks about her relationships. I ask why she didn't marry her charming partner, David Frost, and she says she felt he "needed to have a family and I did not want to have any more children [at that stage]. Also he spent a great deal of time in London, and I did not want to do that."

She has a lovely, bittersweet way of talking, and strangely beautiful eyes. Does she have a boyfriend now? "I have gained the right not to answer that question," she says, effortlessly tough again. And then she tells me that her beautiful apartment is not designed to house a marriage. "I don't want to attract the gigolo mentality. My circumstances are lovely. There is no room for anyone to move in here, emotionally or physically."

Does she ever see Joan Collins in her building? "Oh, I'm not sure if she lives here any more. Dynasty was rather marvellous, you know. It was all about the clothes. The most important thing about the day was wardrobe, and of course I explained to Aaron [Spelling] I didn't want to be on the show unless I could be bitchy." Was the atmosphere as bitchy off screen? "When there was a tense moment it was, but not to be taken too seriously."

She looks forward to new projects. "I would like to sail in my own boat from LA to China.

I would like to visit the home of Catherine the Great. And I would love the next part that I get to be great work like the kind of movie Claudine was." She pauses briefly, weighing her ambition. "The Oscar would be a perk," she decides, "but I just love to do the work."

• The Legs are the Last to Go by Diahann Carroll is published by Amistad at £15.99. To order a copy for £14.99 with free UK p&p go to theguardian.com/bookshop or call 0870 836 0875.