There are many authors that write vampire fiction, but few have the same literary skill as Anne Rice. Rice is known for her world building, deep characters, and writing style that is simultaneously horrific, violent and sexy.
The first read-alike author is Tanith Lee who has written many paranormal series, see the full list here. The series’ Secret books of Venus, Secret books of Paradys and the Blood Opera Sequence is similar to Rice’s Vampire Chronicles in that she creates a realistic world that is dark which supernatural creatures live. Her world-building ability is very similar to Rice, with her in depth descriptions and details.
The second similar author is Jeanne Kalogridis (see her website here), the author of Diaries of the family Dracul trilogy. Kalogridis and Rice both have created realistic and deep characters, vampires who have human characteristics, longings and who are concerned with the morality of their existence. They obsess over good and evil; Rice and Kalogridis have given us tormented vampires who regret their immortality.
Another author that writes with great skill is Elizabeth Kostova, author of The Historian. This novel is considered a Gothic and historical novel, its focus on the setting, world-building and historical facts, makes it similar to Rice’s works.
Jeremiah Jefferson is the author of a vampire series; the books are Voice of the Blood, Wounds, Fiend, A Drop of Scarlet. (see her website here). This novelist is what I would consider a genius–she wrote her first novel in 24 hours. Her writing style is similar to Anne Rice’s but she takes the themes even further; Sex and violence is taken to another level in her novels. Her novels two characters, Orfeo Ricari and Daniel Blum are almost exactly Lestat and Louis (plagiarism much?). Orfeo is a tormented and suicidal vampire that is constantly trying to kill himself, but never actually succeeds. He feels bad for drinking human blood, unlike Daniel who is the most unrepentant sadistic vampire I’ve ever read (even more so than Lestat). If you love the Vampire Chronicles, this series is a good place to go next, though it may be a little too sexy and violent for some.
Interview with the Vampire 