A control device for a vehicle, the vehicle including an internal combustion engine and an electric motor configured to output drive power for traveling, and a clutch disposed between the internal combustion engine and the electric motor, the control device comprises: an electronic control unit configured to: (i) intermittently operate the internal combustion engine, (ii) output a compensation torque from the electric motor so as to cancel a deceleration torque generated when a rotational speed of the internal combustion engine is raised by making the clutch engaged at start-up of the internal combustion engine, (iii) calculate an amount of divergence of an actual rotational speed (Nmg) with respect to a reference rotational speed (Nmgb) of the electric motor at the start-up of the internal combustion engine, and (iv) execute a first correction of correcting at least one of a generation timing of the deceleration torque and a generation timing of the compensation torque at the next start-up of the internal combustion engine based on the amount of divergence, wherein in the first correction, when the actual rotational speed (Nmg) is higher than the reference rotational speed (Nmgb), the electronic control unit is configured to: (i) make the generation timing of the deceleration torque early when the generation timing of the deceleration torque is corrected, and (ii) make the generation timing of the compensation torque late when the generation timing of the compensation torque is corrected, and wherein the internal combustion engine is provided with a fuel injection valve configured to inject fuel directly into a combustion chamber of the internal combustion engine, and the internal combustion engine is configured to execute ignition start-up of injecting fuel from the fuel injection valve into the combustion chamber of a cylinder of the internal combustion engine, and igniting the fuel, the cylinder being in a stopping state in an expansion stroke of the internal combustion engine, and wherein the electronic control unit is configured to execute a second correction of correcting a start timing when the ignition start-up is executed at the next start-up of the internal combustion engine, based on the amount of the divergence. an electronic control unit configured to: (i) intermittently operate the internal combustion engine, (ii) output a compensation torque from the electric motor so as to cancel a deceleration torque generated when a rotational speed of the internal combustion engine is raised by making the clutch engaged at start-up of the internal combustion engine, (iii) calculate an amount of divergence of an actual rotational speed (Nmg) with respect to a reference rotational speed (Nmgb) of the electric motor at the start-up of the internal combustion engine, and (iv) execute a first correction of correcting at least one of a generation timing of the deceleration torque and a generation timing of the compensation torque at the next start-up of the internal combustion engine based on the amount of divergence, wherein in the first correction, when the actual rotational speed (Nmg) is higher than the reference rotational speed (Nmgb), the electronic control unit is configured to: (i) make the generation timing of the deceleration torque early when the generation timing of the deceleration torque is corrected, and (ii) make the generation timing of the compensation torque late when the generation timing of the compensation torque is corrected, and (i) intermittently operate the internal combustion engine, (ii) output a compensation torque from the electric motor so as to cancel a deceleration torque generated when a rotational speed of the internal combustion engine is raised by making the clutch engaged at start-up of the internal combustion engine, (iii) calculate an amount of divergence of an actual rotational speed (Nmg) with respect to a reference rotational speed (Nmgb) of the electric motor at the start-up of the internal combustion engine, and (iv) execute a first correction of correcting at least one of a generation timing of the deceleration torque and a generation timing of the compensation torque at the next start-up of the internal combustion engine based on the amount of divergence, (i) make the generation timing of the deceleration torque early when the generation timing of the deceleration torque is corrected, and (ii) make the generation timing of the compensation torque late when the generation timing of the compensation torque is corrected, and the internal combustion engine is provided with a fuel injection valve configured to inject fuel directly into a combustion chamber of the internal combustion engine, and the internal combustion engine is configured to execute ignition start-up of injecting fuel from the fuel injection valve into the combustion chamber of a cylinder of the internal combustion engine, and igniting the fuel, the cylinder being in a stopping state in an expansion stroke of the internal combustion engine, and wherein the electronic control unit is configured to execute a second correction of correcting a start timing when the ignition start-up is executed at the next start-up of the internal combustion engine, based on the amount of the divergence.