A valve drive mechanism for an engine can include a drive shaft that is configured for rotation about an axis. A valve member is configured to be driven by the rotation of the drive shaft to open and close a valve. A variable valve timing mechanism is positioned at least partially between the valve member and the drive shaft. The variable valve timing mechanism is configured to vary a valve open period of the valve. The valve drive mechanism is configured such that, during a specific operation range, the valve open period includes a main valve open period during which the valve is open in a suction or exhaust stroke, and a sub valve open period during which the valve is open in an expansion or compression stroke.