There are so many good biographies of Martin Luther King that it would be difficult to pick just one. Just pick up one from your library, they should have at least one or two choices for you.
Author Lerone Bennett Jr. wrote an excellent book about Martin Luther King Jr. The title of the book is What Manner of Man: A Biography of Martin Luther King Jr.
Clayborne carson wrote an extremely good autobiography for Martin Luther King. Carson used Dr.king's own diaries, journals, papers, and conducted interviews to assemble this gem.The Autobiography of Martin Luther King.
I would have to say Amy Pastan whom has written many great biographies. Her take on Martin Luther King was fantastic. She was able to bring MLK to life.
Clayborne Carson wrote a great bio on MLK Jr. based on his speeches, notes and other historical documents that might as well have been written in King's words.