An engine control device for an engine provided with a supercharger, the engine comprising a cylinder injection valve for injecting a fuel into a cylinder in the engine; a port injection valve for injecting the fuel into an intake port of the cylinder; and a variable valve actuating mechanism that varies open/close timing of at least one of an intake valve and an exhaust valve of the engine, the engine control device comprising: an injection controller that controls injections of the fuel through the cylinder injection valve and through the port injection valve, on the basis of a rotation speed of the engine; and a variable valve controller that controls the variable valve actuating mechanism on the basis of the rotation speed,wherein when supercharging by the supercharger is activated, the variable valve controller provides a valve overlap period for opening both the intake valve and the exhaust valve, in a first rotation speed region, whereas shortening the valve overlap period in a second rotation speed region of greater rotation speeds than in the first rotation speed region, and the injection controller, in a region where the rotation speed is within the first rotation speed region except for a low rotation speed region where the rotation speed is equal to or smaller than a predetermined rotation speed (Ne 1), causes the fuel to be injected through the cylinder injection valve and through the port injection valve, in the second rotation speed region, causes the fuel to be injected through the cylinder injection valve and through the port injection valve, in a boundary speed region where a rotation speed includes a boundary rotation speed between the first rotation speed region and the second rotation speed region, causes the fuel to be injected through the cylinder injection valve and through the port injection valve, and advances timing for injecting the fuel through the port injection valve at least in the boundary speed region more than in the first rotation region. an injection controller that controls injections of the fuel through the cylinder injection valve and through the port injection valve, on the basis of a rotation speed of the engine; and a variable valve controller that controls the variable valve actuating mechanism on the basis of the rotation speed,wherein when supercharging by the supercharger is activated, the variable valve controller provides a valve overlap period for opening both the intake valve and the exhaust valve, in a first rotation speed region, whereas shortening the valve overlap period in a second rotation speed region of greater rotation speeds than in the first rotation speed region, and the injection controller, in a region where the rotation speed is within the first rotation speed region except for a low rotation speed region where the rotation speed is equal to or smaller than a predetermined rotation speed (Ne 1), causes the fuel to be injected through the cylinder injection valve and through the port injection valve, in the second rotation speed region, causes the fuel to be injected through the cylinder injection valve and through the port injection valve, in a boundary speed region where a rotation speed includes a boundary rotation speed between the first rotation speed region and the second rotation speed region, causes the fuel to be injected through the cylinder injection valve and through the port injection valve, and advances timing for injecting the fuel through the port injection valve at least in the boundary speed region more than in the first rotation region.