A control device for an engine provided with a fuel injection valve disposed within a combustion chamber, a part of which is defined by a piston including a cavity in a crown surface thereof, and configured to directly inject fuel toward the cavity, the control device comprising: a fuel pressure adjustment mechanism for adjusting a fuel pressure of fuel to be supplied to the fuel injection valve; and a controller for controlling the fuel injection valve and the fuel pressure adjustment mechanism, and constituted of a circuitry, wherein the controller is configured to: set an air-fuel ratio of a fuel-air mixture to be generated within the combustion chamber to an air-fuel ratio equal to or leaner than a theoretical air-fuel ratio, based on an operating condition of the engine; output a control signal to the fuel injection valve in such a way as to drive the fuel injection valve, based on the set air-fuel ratio; perform processing of estimating a deposition amount of deposits on an injection hole of the fuel injection valve, based on an operating condition of the engine; output a control signal to the fuel pressure adjustment mechanism in such a way as to increase the fuel pressure, when the estimated deposition amount of deposits exceeds a predetermined value; and restrict the fuel pressure from increasing, even when the estimated deposition amount of deposits exceeds the predetermined value, as far as the set air-fuel ratio is set to an air-fuel ratio leaner than the theoretical air-fuel ratio. a fuel pressure adjustment mechanism for adjusting a fuel pressure of fuel to be supplied to the fuel injection valve; and a controller for controlling the fuel injection valve and the fuel pressure adjustment mechanism, and constituted of a circuitry, wherein the controller is configured to: set an air-fuel ratio of a fuel-air mixture to be generated within the combustion chamber to an air-fuel ratio equal to or leaner than a theoretical air-fuel ratio, based on an operating condition of the engine; output a control signal to the fuel injection valve in such a way as to drive the fuel injection valve, based on the set air-fuel ratio; perform processing of estimating a deposition amount of deposits on an injection hole of the fuel injection valve, based on an operating condition of the engine; output a control signal to the fuel pressure adjustment mechanism in such a way as to increase the fuel pressure, when the estimated deposition amount of deposits exceeds a predetermined value; and restrict the fuel pressure from increasing, even when the estimated deposition amount of deposits exceeds the predetermined value, as far as the set air-fuel ratio is set to an air-fuel ratio leaner than the theoretical air-fuel ratio. set an air-fuel ratio of a fuel-air mixture to be generated within the combustion chamber to an air-fuel ratio equal to or leaner than a theoretical air-fuel ratio, based on an operating condition of the engine; output a control signal to the fuel injection valve in such a way as to drive the fuel injection valve, based on the set air-fuel ratio; perform processing of estimating a deposition amount of deposits on an injection hole of the fuel injection valve, based on an operating condition of the engine; output a control signal to the fuel pressure adjustment mechanism in such a way as to increase the fuel pressure, when the estimated deposition amount of deposits exceeds a predetermined value; and restrict the fuel pressure from increasing, even when the estimated deposition amount of deposits exceeds the predetermined value, as far as the set air-fuel ratio is set to an air-fuel ratio leaner than the theoretical air-fuel ratio.