To evade a generation of a shudder vibration in controlling a lock-up clutch to engage with slip engaging when a vehicle is started.

When a vehicle-starting lock-up clutch control is carried out at vehicle starting, a continuously variable transmission 18 is upshifted from a predetermined first gear ratio γ1 if the lock-up clutch 26 is in a predetermined before-engagement state so that a progress to the engagement may be controlled. After the upshift, the continuously variable transmission 18 is downshifted so that the lock-up clutch 26 may be engaged within a predetermined time T'. Thus, a rotational speed difference of the lock-up clutch is prevented from entering a shudder vibration region near an engagement side where a slip amount NSLP of the lock-up clutch 26 which is concern for, for example, the shudder vibration is small, and the shudder vibration region can be passed promptly.