Provided is a control device of a hybrid vehicle powered by an internal-combustion engine and a motor, wherein a catalyst that purifies exhaust gas is located in an exhaust passage of the internal-combustion engine, and the control device comprises: a learning unit configured to, during operation of the internal-combustion engine, learn a parameter for controlling a rotation speed of the internal-combustion engine so that a rotation speed of the internal-combustion engine during idling operation is equal to a target rotation speed; and a controller configured to stop the internal-combustion engine when a state where a correction amount of the parameter to cause the rotation speed during idling operation to be equal to the target rotation speed is equal to or greater than a predetermined value continues for equal to or greater than a predetermined time period, the correction amount being obtained by learning by the learning unit.