If the a rotational speed difference (Ne−Nt) between an engine speed (Ne) and a turbine speed (Nt) when it is determined that a lock-up ON condition (OFF→ON) is satisfied is large, the lock-up clutch is not engaged but torque reduction control is executed to reduce the engine speed (Ne), thus reducing the rotational speed difference (Ne−Nt) (steps ST13 and ST14). Then, once the rotational speed difference (Ne−Nt) has been reduced to the target rotational speed difference (Nslp), the lock-up clutch is engaged (steps ST15 and ST16). In this manner, excessive heating of the friction material of the lock-up clutch is suppressed which increases the longevity of the friction material.