A valve driving apparatus for an internal combustion engine. Each combustion chamber has a pair of intake ports and a pair of intake valves for selectively opening and closing the intake ports. Each intake valve is driven with a variable amount of valve lift. The apparatus includes a camshaft rotatably supported by the engine, cams, cam followers, a shaft moving mechanism, and brackets. Each cam lifts an associated intake valve in response to rotation of the camshaft. Each cam has a cam nose for lifting a corresponding intake valve. The radius of the cam nose varies in the axial direction. Cam followers transmit movement of the intake cams to the intake valves. The shaft moving mechanism moves the cams relative to the valves in an axial direction of the camshaft thereby varying the amount of valve lift. A lifter structure is provided that is circularly shaped to improve manufacturing accuracy. In another embodiment, the valves are oriented to increase the amount of axial movement that the cam can make, which results in greater optimization of the air intake amount.