In a valve operating apparatus of an engine capable of varying a valve lift characteristic, rotary motion of a drive cam is converted through a motion-conversion linkage including a rocker arm into oscillating motion of a valve actuation member for operating an engine valve. Also provided is a control shaft whose angular position is adjusted depending on an engine operating condition for changing a linkage attitude. The valve actuation member has an arcuate portion curved to bypass the drive shaft. The control shaft has a coaxial shaft portion and an eccentric control cam. The control cam is a fulcrum of oscillating motion of the rocker arm and the coaxial shaft portion of the control shaft is a fulcrum of oscillating motion of the valve actuation member. The fulcrums are laid out in close proximity to each other.