A valve lifter for a three-dimensional cam and a variable valve operating apparatus have enhanced flexibility in the design of a detent mechanism of the valve lifter for the three-dimensional cam, as well as enhanced durability. It is possible to form a thick wall portion which is sufficiently thick without increasing the weight by providing an offset between an outer peripheral surface and an inner peripheral surface of the valve lifter. Therefore, a sufficiently large projection can be mounted without deforming the valve lifter. This structure makes it possible to increase an area contacting a detent groove, reduce the surface pressure, and enhance the durability. The thick wall portion exists longer in an axial direction of the valve lifter, so the detent mechanism can be formed on the outer peripheral surface instead of a top surface. Therefore, the flexibility of design of the detent mechanism can be enhanced.