A three-dimensional cam of a three-dimensional map state, having uncountable cam profiles continuously ranged along a rotation axis direction, and a valve lifter following a cam surface of the three-dimensional cam are included, and a lift characteristic of a valve is continuously controlled by relative motions of the three-dimensional cam and the valve lifter. The three-dimensional cam has cam top portions formed to have a smoothly ranged edge line substantially along the rotation axis direction thereof, and a part of the edge line includes at least one valley portion to take on a row of peaks. The cam peak portion of the cam top portion which forms the valley portion of the edge line is moderately set to be deviated toward a delayed side with reference to the rotation direction of the cam from the other cam peak portions.