A continuously variable transmission with a variator capable of continuously changing a speed ratio and a sub-transmission mechanism connected to an output side of the variator and configured to switch a gear position by changing engaged states of a plurality of frictional engagement elements (32, 33, 34), comprising: coordinated shift means configured to perform a coordinated shift of changing a speed ratio of the variator in a direction opposite to a speed ratio changing direction of the sub-transmission mechanism in shifting the sub-transmission mechanism; power-on downshift determination means configured to determine whether or not the shift of the sub-transmission mechanism is a power-on downshift caused by the depression of an accelerator pedal in the case of performing the coordinated shift; feedback control means configured to control a capacity of the frictional engagement element (32, 33, 34) of the sub-transmission mechanism to be released according to a rotation speed feedback correction amount caused by a difference between a target input rotation speed and an actual input rotation speed of the sub-transmission mechanism if the shift of the sub-transmission mechanism is determined to be a power-on downshift; characterized by rotation stagnation determination means configured to determine whether or not an input rotation speed of the sub-transmission mechanism is stagnant; and addition means configured to add a rotation speed change rate feedback correction amount caused by a difference between a target input rotation speed change rate and an actual input rotation speed change rate of the sub-transmission mechanism to the rotation speed feedback correction amount when the input rotation speed is determined to be stagnant. coordinated shift means configured to perform a coordinated shift of changing a speed ratio of the variator in a direction opposite to a speed ratio changing direction of the sub-transmission mechanism in shifting the sub-transmission mechanism; power-on downshift determination means configured to determine whether or not the shift of the sub-transmission mechanism is a power-on downshift caused by the depression of an accelerator pedal in the case of performing the coordinated shift; feedback control means configured to control a capacity of the frictional engagement element (32, 33, 34) of the sub-transmission mechanism to be released according to a rotation speed feedback correction amount caused by a difference between a target input rotation speed and an actual input rotation speed of the sub-transmission mechanism if the shift of the sub-transmission mechanism is determined to be a power-on downshift; characterized by rotation stagnation determination means configured to determine whether or not an input rotation speed of the sub-transmission mechanism is stagnant; and addition means configured to add a rotation speed change rate feedback correction amount caused by a difference between a target input rotation speed change rate and an actual input rotation speed change rate of the sub-transmission mechanism to the rotation speed feedback correction amount when the input rotation speed is determined to be stagnant.