An assist handle apparatus for a vehicle having a mounting plate positioned at a handgrip may include a damping mechanism having a hinge pin connected to the handgrip; hinge ends positioned at first and second sides of the mounting plate, wherein a damper seat is formed in a space defined between the hinge ends; a damper that is inserted in the damper seat with the hinge pin passing through the damper and the hinge ends, the damper having first and second damping ends protruding at a first side and a second side of an outer circumference of the damper respectively; and a stopper that is formed on an inner side of a hinge portion of the handgrip, wherein the stopper damps rotation shock in both rotation directions of the handgrip when the stopper selectively contacts with the first damping end or the second damping end according to rotation of the handgrip.