A method is developed to simulate the flexible fiber. The developed method is based on the lattice Boltzman scheme and ball and socket model of fiber. A half frog algorithm for rotation is modified to include the constraint force. The rotation matrix is linear zed with respect to the constraint forces. Subquently, equations for the constraint forces at joint point are solved. Simulations of sedimentation of a flexible cylindrical fiber in moderate Reynolds number flows are reported. It shows that fiber migrates not only in the gravity depiction but also in the horizontal direction. The migration path depends on the initial fiber orientation and positions. It could move to wall initially, and then come back to the center of the channel due to wall repulsion. At a large Reynolds number, the long body will turn to horizontal direction while at a small Reynolds number it will align with gravity. The fiber flexibility has a profound effect on migration and terminal speed.