In a shift control apparatus of a continuously variable transmission (CVT) configured to steplessly vary a torque, the control apparatus employs an acceleration intention determination section for determining the presence or absence of a driver's acceleration intention, a shift mode setting section for setting a shift-control mode from a normal mode to an acceleration mode in the presence of the driver's acceleration intention, a shift speed setting section for setting a shift speed based on a target transmission ratio and a vehicle speed, and a shift control section for controlling a shift of the CVT. Also provided is a shift speed correction section for correcting the shift speed for an initial downshift in the acceleration mode to a shift speed slower than the shift speed set by the shift speed setting section, only when a demanded degree of the driver's acceleration intention is small.