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 at least a load on the engine; and a variable valve controller that controls the variable valve actuating mechanism on the basis of the load, wherein the injection controller: in a low load operating state, causes the fuel to be injected through the port injection valve, in an intermediate load operating state, causes the fuel to be injected through the cylinder injection valve during an intake stroke, and causes the fuel to be injected through the port injection valve, and in a high load operating state, sets an amount of the fuel to be injected through the port injection valve to 0 when the engine is at a low rotation speed, and increases a ratio of an amount of the fuel to be injected through the port injection valve, as a rotation speed of the engine increases, and causes the fuel to be injected through the cylinder injection valve at least during an intake stroke and during a compression stroke, and the variable valve controller provides a valve overlap period for opening both the intake valve and the exhaust valve, at least in the high load operating state, and extends the valve overlap period when the engine is at the low rotation speed with respect to the valve overlap period when the engine is at another, higher rotation speed, in the high load operating state. an injection controller that controls injections of the fuel through the cylinder injection valve and through the port injection valve, on the basis of at least a load on the engine; and a variable valve controller that controls the variable valve actuating mechanism on the basis of the load, wherein the injection controller: in a low load operating state, causes the fuel to be injected through the port injection valve, in an intermediate load operating state, causes the fuel to be injected through the cylinder injection valve during an intake stroke, and causes the fuel to be injected through the port injection valve, and in a high load operating state, sets an amount of the fuel to be injected through the port injection valve to 0 when the engine is at a low rotation speed, and increases a ratio of an amount of the fuel to be injected through the port injection valve, as a rotation speed of the engine increases, and causes the fuel to be injected through the cylinder injection valve at least during an intake stroke and during a compression stroke, and the variable valve controller provides a valve overlap period for opening both the intake valve and the exhaust valve, at least in the high load operating state, and extends the valve overlap period when the engine is at the low rotation speed with respect to the valve overlap period when the engine is at another, higher rotation speed, in the high load operating state. in a low load operating state, causes the fuel to be injected through the port injection valve, in an intermediate load operating state, causes the fuel to be injected through the cylinder injection valve during an intake stroke, and causes the fuel to be injected through the port injection valve, and in a high load operating state, sets an amount of the fuel to be injected through the port injection valve to 0 when the engine is at a low rotation speed, and increases a ratio of an amount of the fuel to be injected through the port injection valve, as a rotation speed of the engine increases, and causes the fuel to be injected through the cylinder injection valve at least during an intake stroke and during a compression stroke, and