An apparatus for controlling a clutch of a motor vehicle connected to an engine and having a driving and a driven rotating member. The apparatus is capable of controlling an amount of slip of the clutch during starting of the vehicle. The apparatus includes: an engine torque determining device for determining a torque of the engine; a clutch speed monitoring device for determining whether a speed of the driven rotating member has been raised to a level substantially equal to a speed of the engine; a first slip control device for controlling the amount of slip of the clutch such that a clutch torque to be transmitted through the clutch is smaller than the engine torque by a predetermined amount, before the clutch speed monitoring device determines that the speed of the driven rotating member has been raised to the level equal to the engine speed; and a fully engaging device for fully engaging the clutch when the clutch speed monitoring device determines that the speed of the driven rotating member has been raised to the level.