Sawyer killed him.
Essentially, for some reason, Ben looked into everything about the Losties via "what's his face" who was at the flame. Mikhov, or something like that. He learned Locke could walk upon reaching the island, and saw him as a threat. From there, they learned where Anthony Cooper was, in Tallahasse, and actually kidnapped him and brought him to the island.
Once Ben and Locke met up in the "Others'" camp, it was revealed that Locke might be the leader. Apparently, Ben brought Locke's father to the island to force Locke to kill him, saying Locke's daddy issues were a rock in his path to being fearless leader. It was basically a ploy by Ben to remain in power, as Ben hoped Locke wouldn't go through with killing him. Richard basically told Locke this, and gave him a folder with information on Sawyer, including his real name, James Ford, and the reason why he goes by Sawyer: His family was killed by a con man using the name Sawyer. That man's real name was Anthony Cooper, and just happened to be Locke's father.
Since Locke had reservations about killing his father, Locke took his father to the Black Rock and tied him up to in a room on the boat, then went back to the Losties' camp to find Sawyer. He told Sawyer he had Ben tied up on the Black Rock, and he needed Sawyer to kill him. When they arrived, Locke locked Sawyer in the room with Anthony Cooper, and after a little bit of talking, Sawyer figured out who he was and killed him. Locke took the body back to the Others, and then resumed the process of becoming their leader.