PURPOSE: To obtain a variable speed position corresponding to the low μ road surface condition by correcting a target torque ratio based on a detected road surface condition factor, and outputting a variable speed command on the bases of a corrected target torque ratio and an actual torque ratio.

CONSTITUTION: In a control device of a vehicle automatic transmission, a road surface condition detection unit A15 sets a road surface condition factor from the road surface condition detected by a low μ road detecting means 109. Then, a variable speed judgement processing unit B5 corrects a target torque determined by an optimum fuel cost-maximum power judgement unit B3 by the use of the road surface condition factor, and determines variable speed direction by a corrected target torque ration and an actual torque ratio obtained by a calculation unit B2 to output a variable speed command to a CVT variable speed motor 7, and further output a CVT unit variable speed calculated by a calculation unit B4 to the CVT variable speed motor. Starting of a vehicle on the low μ road can thus be smoothly performed without causing slip.