A device for varying a valve timing and lift for an internal combustion engine comprises a first valve lifter and a second valve lifter, and an oil pressure chamber being defined between the first valve lifter and the second valve lifter. The flow of oil from the oil pressure chamber is continuously and steplessly controlled through a high-speed response control valve in an oil extraction passage. While the oil is being removed, the valve does not lift. When the high-speed response control valve is closed, the first valve lifter and the second valve lifter move together and the valve begins to lift. By controlling the action of the actuator of the high-speed response control valve, the valve timing and lift of the poppet valve can be controlled to the optimum ones matching the engine operating conditions.