An intake side phase varying mechanism varies an open/close timing of an intake valve, and an exhaust side phase varying mechanism varies an open/close timing of an exhaust valve. Before starting the engine, one of the intake and exhaust side phase varying mechanisms is caused to keep a first position wherein the intake and exhaust valves show the largest valve overlap therebetween and the other of the mechanisms is caused to keep a second position wherein the intake and exhaust valves show the smallest valve overlap therebetween. A controller is configured to carry out, after starting the engine, causing the selected one of the intake and exhaust side phase varying mechanisms to be actually controlled to the first position and causing the other to be actually controlled to the second position.