A control system for an engine including a cylinder, an intake passage, an exhaust passage, an intake port communicating the intake passage to the cylinder, an intake valve configured to open and/or close the intake port, an exhaust port communicating the exhaust passage to the cylinder, an exhaust valve configured to open and/or close the exhaust port, an injector configured to inject fuel into the cylinder, and a spark plug configured to ignite a mixture gas containing the fuel injected by the injector and air, the engine being configured to execute partial compression-ignition combustion in which the mixture gas is spark-ignited with the spark plug to be partially combusted by spark ignition combustion and the remaining mixture gas self-ignites to be combusted by compression ignition combustion, comprising: an intake phase-variable mechanism configured to simultaneously change an open timing and a close timing, or change a phase of the intake valve; and a controller configured to control at least the intake phase-variable mechanism and the spark plug, wherein the controller is configured to control the intake phase-variable mechanism to form a gas-fuel ratio lean environment in which burnt gas remains inside the cylinder and an air-fuel ratio that is a ratio of air to fuel inside the cylinder is substantially or near a stoichiometric air-fuel ratio, and control the spark plug to spark-ignite the mixture gas so as to combust by the partial compression-ignition combustion at a given timing, characterized in that the controller is configured to control, while the engine operates within a given first operating range where the partial compression-ignition combustion is carried out under the gas-fuel ratio lean environment, the intake phase-variable mechanism to retard, as an engine speed increases at a constant engine load, the close timing of the intake valve on a retarding side of a bottom dead center of intake stroke and the open timing of the intake valve on an advancing side of a top dead center of exhaust stroke, so that in a segment of the first operating range where the engine speed is higher than a particular engine speed, the open timing and the close timing of the intake valve are retarded as the engine speed increases, and in a segment of the first operating range where the engine speed is lower than the particular engine speed, the open timing and the close timing of the intake valve are maintained at constant timings. an intake phase-variable mechanism configured to simultaneously change an open timing and a close timing, or change a phase of the intake valve; and a controller configured to control at least the intake phase-variable mechanism and the spark plug, wherein the controller is configured to control the intake phase-variable mechanism to form a gas-fuel ratio lean environment in which burnt gas remains inside the cylinder and an air-fuel ratio that is a ratio of air to fuel inside the cylinder is substantially or near a stoichiometric air-fuel ratio, and control the spark plug to spark-ignite the mixture gas so as to combust by the partial compression-ignition combustion at a given timing, characterized in that the controller is configured to control, while the engine operates within a given first operating range where the partial compression-ignition combustion is carried out under the gas-fuel ratio lean environment, the intake phase-variable mechanism to retard, as an engine speed increases at a constant engine load, the close timing of the intake valve on a retarding side of a bottom dead center of intake stroke and the open timing of the intake valve on an advancing side of a top dead center of exhaust stroke, so that in a segment of the first operating range where the engine speed is higher than a particular engine speed, the open timing and the close timing of the intake valve are retarded as the engine speed increases, and in a segment of the first operating range where the engine speed is lower than the particular engine speed, the open timing and the close timing of the intake valve are maintained at constant timings.