A lift-variable valve-operating system for an internal combustion engine, comprising: subsidiary cams which are swingably supported on a movable support shaft capable of being displaced within a plane perpendicular to a rotational axis of a valve-operating cam, and which are swung following the valve-operating cam; and rocker arms each operatively connected to an engine valve and operated following the subsidiary cams, operating characteristics including a lift amount of the engine valve being changed by displacing the movable support shaft, wherein the system further includes a control arm carried in an engine body to be capable of turning about a turning axis parallel to a rotational axis of the valve-operating cam, wherein the movable support shaft having an axis parallel to the turning axis of the control arm is retained on the control arm at a location offset from the turning axis, wherein a hydraulic tappet is mounted in the control arm to support one end of each of the rocker arms, and wherein a valve abutment portion provided at the other end of each of the rocker arms is in abutment against an upper end of a stem of the engine valve. Thus, it is possible to enhance the control accuracy in a state in which the lift amount of the engine valve is controlled to be low.