A control device of an FR hybrid vehicle is provided with: a drive source that contains at least an engine (Eng); and a second brake (B2) that is fastened when a D range is selected. In the range of starting of fastening control of the second brake (B2), when the parameters (rate of input rotational frequency change and amount of motor torque change) that change along with the rotational fluctuation of the engine (Eng) become at least a predetermined threshold, it is judged that the second brake (B2) has started fastening. When in a state wherein the rotational fluctuations of the engine (Eng) can be determined to be large, the absolute value of the predetermined threshold is set to a value that is larger than when in a state wherein the rotational fluctuations of the engine (Eng) can be determined to be small.