This is a great question. There are many reasons for Dr. Martin Luther King's approach to social change. However, I believe that King knew that the only way to effect a change that will last is by winning people over to the side of justice rather than winning people over by force. This is why one of the most memorable things he stated was:
"The goal is not to defeat or humiliate the opponent but rather to win him or her over to understanding new ways to create cooperation and community."
A little reflection will show the great logic in this. Unless you win people over to embrace your cause, you will never have a society that is able to live in harmony. Might will make right; hearts will not be won over.
Also we can say that King learned some great things from Gandhi. In some sense, Gandhi was a mentor. The great Gandhi stated:
"Rivers of blood may have to flow before we gain our freedom, but it must be our blood."
King knew that the best way to win people over to his cause was when they saw the injustices of their ways in the suffering of peaceful activists. Finally, I am certainly that behind all of this, he learned these principles from the Bible as a minister. The theology of 1 Peter is most fitting.
In addition to these philosophical reasons, King had solid historical and sociological reasons for advocating non-violence. King knew that a group that was in the position African Americans faced in the United States could not prevail through violence. He knew that many white Americans would be suspicious and even wary of African Americans. He knew that this fear would be exacerbated by any violence in the movement. He also knew (in part from the example of Gandhi's movement in India) that a social movement needed to get the approval of those who had the power. He realized that the only way to get this approval was to be nonviolent in the face of violence and abuse. He knew that African Americans would have to look like the "good guys" in order to get white Americans to side with them and to allow them to have civil rights.