A hydraulic valve driving device includes a valve actuator operable to drive an engine valve, a hydraulic pump that generates the oil pressure for the valve actuator, a hydraulic pump driving motor that drives the hydraulic pump, and a starter motor. At the time of engine starting, after the hydraulic pump is driven by the hydraulic pump driving motor while the crank is stopped in the first engine-starting mode, and then the crank and the hydraulic pump are driven by the starter motor in the second engine-starting mode.