A speed-ratio control apparatus for controlling a speed ratio of a continuously variable transmission of a vehicle, such that an actual input speed of the transmission coincides with a target input speed, the apparatus including an acceleration-requirement determining portion operable to determine whether non-rapid acceleration or rapid acceleration of the vehicle is required by a vehicle operator, and a target-input-speed setting portion operable, upon determination of the operator's requirement for the non-rapid acceleration, to implement an instantaneous stepping increase of the target input speed to a first transient target value, (ii) hold the target input speed at the first transient target value in a first portion of a rapid shifting period, (iii) instantaneously reduce, at the end of the first portion of the rapid shifting period, the target input speed to an initial value of a second transient target value which initial value is close to the actual input speed and lower than the first transient target value, and (iv) gradually increase, in a second portion of the rapid shifting period, the target input speed back toward the first transient value, and upon determination of the operator's requirement for the rapid acceleration, the target-input-speed setting portion holding the target input speed at the first transient target input speed during the rapid shifting period, without setting at the second transient target value.