An engine unit includes a valve driving mechanism in which a cam having its cam profile axially varying continuously is slid along the axis of the cam shaft to control continuously a lift characteristic of an intake valve to be steplessly variable. In the control device of the engine, when the engine is, determined to be in a idling state by an idling-state determining unit, a target cam position is obtained according to a target valve lift amount calculated based on the cooling water temperature by a target cam position calculated unit, and the target cam position is corrected according to atmospheric pressure, an engine oil temperature, an ATF temperature, and an intake temperature, so that an engine rotation will be stabilized in the idling state.