A control apparatus of an automatic transmission having first and second frictional engagement elements that achieve higher and lower speed gear stages respectively, includes a target value determination section setting a rotation speed difference between input and output sides of the frictional engagement element, a total torque capacity calculation section calculating a total torque capacity, a distribution ratio determination section setting a distribution ratio of the total torque capacity to the first and second frictional engagement elements, an individual torque capacity calculation section calculating individual torque capacities respectively required of the first and second frictional engagement elements, and an engagement control section controlling engagement conditions of the first and second frictional engagement elements in accordance with the individual torque capacity. The automatic transmission realizes a down-shift by changeover between first and second frictional engagement elements based on the individual torque capacity during a vehicle power-off travel.