An automatic transmission control apparatus is provided with a control scheme that focuses on the rotational speed differences of the frictional engaging elements and the distribution of torque transferred by the frictional engaging elements. When the automatic transmission is upshifted while in a power-off state, the individual torque capacity of a frictional engaging element being released and the individual torque capacity of a frictional engaging element being connected are corrected by adding a prescribed torque capacity amount to each of the individual torque capacities during an inertia phase of the shift control in which a compensation is executed for inertia related to changing the gear ratio. In this way, frictional losses are induced in the frictional engaging elements so as to absorb the inertia torque and lower the input rotational speed more quickly.