A control device for an engine including a combustion chamber, an ignition plug disposed in the combustion chamber, and an injector configured to inject fuel into the combustion chamber, the control device comprising a processor configured to control the ignition plug and the injector so that partial compression ignition combustion, in which spark ignition combustion of a portion of a mixture gas inside the combustion chamber is carried out by flame propagation from an ignited point of the ignition plug and compression ignition combustion of the remaining mixture gas is carried out by self-ignition, is performed, and determine whether there is a request for an ignition retard for retarding an ignition timing of the ignition plug, wherein the processor is configured to, execute, when the partial compression ignition combustion is performed and there is not the request for the ignition retard, a control in which the entire fuel to be injected in one cycle is injected in an intake stroke and spark ignition is carried out at a basic ignition timing set according to an operating condition of the engine, and determine that there is the request for the ignition retard based on the existence of a torque-down request for temporarily reducing an output torque of the engine, wherein the processor is configured to execute, when the partial compression ignition combustion is performed and there is the request for the ignition retard, a control in which an injection is performed in an intake stroke, a portion of the entire fuel is injected in a compression stroke, and the ignition timing is retarded from the basic ignition timing. a processor configured to control the ignition plug and the injector so that partial compression ignition combustion, in which spark ignition combustion of a portion of a mixture gas inside the combustion chamber is carried out by flame propagation from an ignited point of the ignition plug and compression ignition combustion of the remaining mixture gas is carried out by self-ignition, is performed, and determine whether there is a request for an ignition retard for retarding an ignition timing of the ignition plug, control the ignition plug and the injector so that partial compression ignition combustion, in which spark ignition combustion of a portion of a mixture gas inside the combustion chamber is carried out by flame propagation from an ignited point of the ignition plug and compression ignition combustion of the remaining mixture gas is carried out by self-ignition, is performed, and determine whether there is a request for an ignition retard for retarding an ignition timing of the ignition plug, wherein the processor is configured to, execute, when the partial compression ignition combustion is performed and there is not the request for the ignition retard, a control in which the entire fuel to be injected in one cycle is injected in an intake stroke and spark ignition is carried out at a basic ignition timing set according to an operating condition of the engine, and determine that there is the request for the ignition retard based on the existence of a torque-down request for temporarily reducing an output torque of the engine, wherein the processor is configured to execute, when the partial compression ignition combustion is performed and there is the request for the ignition retard, a control in which an injection is performed in an intake stroke, a portion of the entire fuel is injected in a compression stroke, and the ignition timing is retarded from the basic ignition timing.