A steplessly variable vehicle transmission has a speed ratio control system including an electronic control unit which functions to calculate a required vehicle acceleration rate based on the position of an engine control foot pedal and the rate of change of the position of the foot pedal. The control unit further calculates an engine output power required for accomplishing the vehicle acceleration rate, as well as the engine speed under which the required engine output power can be obtained with the given position of the engine control foot pedal. Further, the control unit produces an output for controlling the speed ratio of the transmission so that the required engine speed is obtained.