Method and apparatus for controlling a continuously variable transmission for a vehicle for transmitting an output of an engine of the vehicle to its drive wheels, comprising a step or device for detecting an engine speed, a step or device for detecting a vehicle running speed, a step or device for sensing a vacuum pressure in an intake manifold connected to the engine, a step or device for determining an actual engine output based on the detected engine speed and the sensed intake vacuum pressure, a step or device for determining a target engine speed based on the detected vehicle running speed and the determined actual engine output, and according to a predetermined relation among the target engine speed, the vehicle running speed and the actual engine output, said relation being predetermined to attain a required output of the engine with a minimum specific fuel consumption, and further comprising a step or device for controlling the speed ratio such that the detected engine speed coincides with the target engine speed.