In a control apparatus for a vehicle power transmission mechanism (automatic transmission) having a transmission equipped with at least an input shaft connected to a drive source mounted on a vehicle, an output shaft connected to the input shaft via a speed ratio change mechanism, and a clutch (start clutch) which transmits a rotation of the output shaft to driven wheels and whose engaging force is regulated, a clutch output rotation change rate is calculated, and the clutch engaging force is corrected to decrease when the calculated output rotation change rate is a positive value, and the clutch engaging force is corrected to increase when the calculated output rotation change rate is a negative value, thereby enabling to suppress clutch juddering occurred due to a difference between input and output rotational speeds of the clutch.