A control device for an engine, the control device being applicable to an engine including a plurality of cylinders, and configured to selectively execute a reduced-cylinder operation by setting one or some of the plurality of cylinders as idle cylinders to be brought into idle states, and an all-cylinder operation for operating all the cylinders, the control device comprising: a hydraulic valve-stopping mechanism which holds an intake valve and an exhaust valve of the idle cylinder in closed states in the reduced-cylinder operation; a hydraulic phase control mechanism making a phase of the intake valve or the exhaust valve of the engine variable; a control unit which controls the hydraulic valve-stopping mechanism and the hydraulic phase control mechanism; and an air amount adjustment unit capable of adjusting an amount of air supplied to the engine, wherein in response to establishment of a reduced-cylinder operation execution condition as a condition for executing the reduced-cylinder operation, the control unit is configured to cause the hydraulic phase control mechanism to execute a phase change to the intake valve or the exhaust valve, and subsequently, cause the hydraulic valve-stopping mechanism to bring the intake valve and the exhaust valve of the idle cylinders to be held closed, wherein in response to establishment of the reduced-cylinder operation execution condition, the control unit is configured to cause the hydraulic phase control mechanism to execute the phase change to the intake valve or the exhaust valve, and subsequently cause the hydraulic valve-stopping mechanism to start the oil pressure adjustment for bringing the intake valve and the exhaust valve of the idle cylinders to be held closed, wherein after the oil pressure applied to an oil passage communicated with the hydraulic valve-stopping mechanism reaches a predetermined target oil pressure, the control unit is configured to cause the air amount adjustment unit to start the air amount adjustment, and wherein after the oil pressure applied to the oil passage communicated with the hydraulic valve-stopping mechanism reaches the predetermined target oil pressure, the control unit is configured to cause the hydraulic phase control mechanism to change the phase of the intake valve or the exhaust valve to a target phase in the reduced-cylinder operation, and subsequently cause the air amount adjustment unit to start the air amount adjustment. a hydraulic valve-stopping mechanism which holds an intake valve and an exhaust valve of the idle cylinder in closed states in the reduced-cylinder operation; a hydraulic phase control mechanism making a phase of the intake valve or the exhaust valve of the engine variable; a control unit which controls the hydraulic valve-stopping mechanism and the hydraulic phase control mechanism; and an air amount adjustment unit capable of adjusting an amount of air supplied to the engine, wherein in response to establishment of a reduced-cylinder operation execution condition as a condition for executing the reduced-cylinder operation, the control unit is configured to cause the hydraulic phase control mechanism to execute a phase change to the intake valve or the exhaust valve, and subsequently, cause the hydraulic valve-stopping mechanism to bring the intake valve and the exhaust valve of the idle cylinders to be held closed, wherein in response to establishment of the reduced-cylinder operation execution condition, the control unit is configured to cause the hydraulic phase control mechanism to execute the phase change to the intake valve or the exhaust valve, and subsequently cause the hydraulic valve-stopping mechanism to start the oil pressure adjustment for bringing the intake valve and the exhaust valve of the idle cylinders to be held closed, wherein after the oil pressure applied to an oil passage communicated with the hydraulic valve-stopping mechanism reaches a predetermined target oil pressure, the control unit is configured to cause the air amount adjustment unit to start the air amount adjustment, and wherein after the oil pressure applied to the oil passage communicated with the hydraulic valve-stopping mechanism reaches the predetermined target oil pressure, the control unit is configured to cause the hydraulic phase control mechanism to change the phase of the intake valve or the exhaust valve to a target phase in the reduced-cylinder operation, and subsequently cause the air amount adjustment unit to start the air amount adjustment.