A rocker arm (63) is provided with a valve connecting portion (63a) into which tappet screws (70) abutting against a pair of engine valves (19) are screwed so that their advance/retract positions can be adjusted, and the rocker arm (63) has a cam abutting portion (65) which abuts against a valve operating cam (69) and is interlocked and connected to the engine valves (19). The rocker arm (63) turnably connects to one end of a first link arm (61) turnably supported at a fixed position of an engine body and to one end of a second link arm turnably supported by a displaceable movable support shaft (68a). The rocker arm (63) is formed so that the valve connecting portion (63a) has a larger width in a direction along a rotating axis of the valve operating cam (69) than in the remaining part. This enables the lift amount of the engine valves to be continuously varied. It is also possible to reduce the size of the system, while ensuring follow-up ability of the opening/closing operations.