A multi-link variable compression ratio engine is provided with a crankshaft, a piston, a control shaft, a linkage, a motor and a reduction mechanism. The crankshaft moves the piston within an engine cylinder. The control shaft has an eccentric axle eccentric relative to its center-axis. The linkage operatively connects the piston to the crankshaft and the crankshaft to the eccentric axle of the control shaft. The motor rotates the control shaft so a top-dead-center position of the piston changes to vary compression ratios by changing the positions of the eccentric axle and the linkage. The reduction mechanism couples the motor to the control shaft to transmit a reduced rotation of the motor to the control shaft so a reduction ratio of a rotation angle of the motor to a rotation angle of the control shaft is less at high-compression ratios than at intermediate compression ratios.