An apparatus for controlling a continuously variable transmission for use with an automotive vehicle. The transmission is operable at a variable speed ratio for transmitting a drive from its input shaft to its output shaft. A target value for the speed of rotation of the input shaft of the transmission is calculated based on the sensed vehicle operating conditions including vehicle acceleration. A correction factor per predetermined unit time is calculated based on the sensed vehicle acceleration when the sensed vehicle acceleration exceeds a threshold value with the accelerator pedal released. The correction factor is added to the target input shaft speed value to correct the target input shaft speed value in an increasing direction at intervals of the predetermined unit time. The threshold value is decreased as the vehicle speed increases. The speed ratio is controlled to bring the input shaft speed into coincidence with the corrected target value.