A valve operating device for an internal combustion engine enabling both valve timing and valve lift characteristic to be varied depending on engine operating conditions includes intake and exhaust camshafts, an eccentric cam fixed to a first one of the intake and exhaust camshafts so that an axis of the eccentric cam is eccentric to an axis of the first camshaft. A rockable cam is supported on the first camshaft so that the rockable cam rotates or oscillates about the axis of the first camshaft. A rocker arm is oscillatingly supported on an outer periphery of the eccentric cam so that a center of an oscillating motion of the rocker arm revolves around the axis of the first camshaft. Also provided is a control shaft variably controlling the center of the oscillating motion of the rocker arm.