A control apparatus of an automatic transmission has an engagement part, a power-ON/OFF state judgment section and a control section controlling a capacity of the engagement part. The control section compares an actual input revolution speed difference absolute value of an absolute value of a difference between an input revolution speed when engaged and an actual input revolution speed with a target input revolution speed difference absolute value of an absolute value of a difference between the input revolution speed when engaged and a target input revolution speed, then a deviation is determined by subtracting the target input revolution speed difference absolute value from the actual input revolution speed difference absolute value. When the deviation is positive, the capacity is increased. When the deviation is negative, the capacity is reduced. When the deviation is zero, a previous capacity that is set before the comparison of the both absolute values is maintained.