A control apparatus of a parallel hybrid leaning vehicle including an internal combustion engine serving as a drive source for travel of the parallel hybrid leaning vehicle, and an electric motor serving as a drive source for travel of the parallel hybrid leaning vehicle, and a clutch disposed in a power transmission route between the engine and a drive wheel, the control apparatus comprising: a travel mode request section that requests one travel mode selected from a plurality of travel modes including i) an EV mode in which the engine is stopped and the electric motor is operated with the clutch disengaged, ii) a transient mode in which the engine is operated with the clutch disengaged, and iii) a HEV mode in which the engine and the electric motor are operated with the clutch engaged; and a travel mode setting section that determines whether a steady turning condition is satisfied and that, depending on a result of the determination, sets the travel mode requested by the travel mode request section as a travel mode to be executed, the steady turning condition including a first condition that the vehicle is determined to be in a predetermined steady turning state or a second condition that the vehicle is predicted to remain in the steady turning state for at least a predetermined time, wherein characterized in that: when the travel mode request section requests the transient mode during travel in the EV mode, the travel mode setting section, upon determining that the steady turning condition is satisfied, sets the transient mode as the travel mode to be executed, and when the travel mode request section requests the transient mode during travel in the EV mode, the travel mode setting section, upon determining that the steady turning condition is not satisfied, prohibits the transient mode from being set as the travel mode to be executed. a travel mode request section that requests one travel mode selected from a plurality of travel modes including i) an EV mode in which the engine is stopped and the electric motor is operated with the clutch disengaged, ii) a transient mode in which the engine is operated with the clutch disengaged, and iii) a HEV mode in which the engine and the electric motor are operated with the clutch engaged; and a travel mode setting section that determines whether a steady turning condition is satisfied and that, depending on a result of the determination, sets the travel mode requested by the travel mode request section as a travel mode to be executed, the steady turning condition including a first condition that the vehicle is determined to be in a predetermined steady turning state or a second condition that the vehicle is predicted to remain in the steady turning state for at least a predetermined time, wherein characterized in that: when the travel mode request section requests the transient mode during travel in the EV mode, the travel mode setting section, upon determining that the steady turning condition is satisfied, sets the transient mode as the travel mode to be executed, and when the travel mode request section requests the transient mode during travel in the EV mode, the travel mode setting section, upon determining that the steady turning condition is not satisfied, prohibits the transient mode from being set as the travel mode to be executed. when the travel mode request section requests the transient mode during travel in the EV mode, the travel mode setting section, upon determining that the steady turning condition is satisfied, sets the transient mode as the travel mode to be executed, and when the travel mode request section requests the transient mode during travel in the EV mode, the travel mode setting section, upon determining that the steady turning condition is not satisfied, prohibits the transient mode from being set as the travel mode to be executed.