PURPOSE: To perform gear shift control hardly to produce a slip caused by an increase in torque at down-shift in a condition that the surface of a road is slippery with snow or others.

CONSTITUTION: An outside air temperature, a quantity of raindrop, and the rotation speeds of a driving wheel and a driven wheel are detected, coefficient of lowμ road Kμ is calculated by finding respective correction factors Kt, Kr, Ks based on those detected values, and the shift down running speed is corrected to the lower speed side according to the coefficient of lowμ road Kμ, so as to make it hard to perform down-shift.