Who are the most famous writers that use dialogue as the main of narration in the story? (except Hemingway)
I would add Cormac McCarthy to the list as a contemporary writer who depends on dialogue as the main tool for developing character. The Road is an excellent example, and his earlier works such as Blood Meridian and The Border Trilogy all depend to a great extent on dialogue and recreation of characters' thoughts.
F. Scott Fitzgerald generally employs much meaningful dialogue. In his story, "The Cut-Glass Bowl," for instance, much of the story is dialogue which advances the plot. Another story rich in dialogue is Fitzgerald's "The Ice Palace.
Another delightful story, rich in a charged dialogue is "Roman Fever" by Edith Wharton.
I think you could look at Faulkner for some examples of this technique. Even though the use of dialogue isn't his primary device for characterization, it is certainly relevant in stories such as "Barn Burning" or "A Rose for Emily." And it is certainly something to consider in his longer works, such as As I Lay Dying.
If you don't have to confine yourself to American authors, Jane Austen immediately comes to mind as an author who used dialogue and scenes of conversations to characterize her characters. This is easily seen in Pride and Prejudice.
What about Alexander Dumas? He wrote the three musketeers series. Although there are brief parts in each novel where the author speaks like a narrator; the majority of the works are driven by dialogue.
If you are looking for something that is only dialogue, you might look at playwrights like Shakespeare.
Thanks a lot Wannam, I am looking for writers in English literature , mostly American writers from 1900s to 1980s, who can be compared to Hemingway in style, that is using of dialogue as the main narration device.