A method and an apparatus for controlling a clutch of a vehicle include determining whether a vehicle is moving under a condition in which a gearshift is coupled to the clutch. A clutch torque is learned in which the clutch is maintained in a micro-slip state by decreasing a target clutch torque for a corresponding gear level when it is determined that the vehicle is moving under the condition in which the gearshift is coupled to the clutch. Learning reliability is calculated by reflecting a difference between an engine torque and clutch torque. The clutch is maintained in the micro-slip state for the clutch torque learning or converting the clutch into a lock-up state, depending on a learning reliability level.