A control device for a compression self-ignition engine includes a fuel injection system and an injection controller. While the engine is operated by CI combustion under a given first condition, a first injection is carried out in which fuel is injected at a first timing in a compression stroke and at which the fuel goes toward a part radially outward of a cavity formed in a crown surface of a piston, and a second injection is suspended. While the engine is operated by the CI combustion under a second condition in which a temperature inside a combustion chamber at a close timing of an intake valve becomes lower than the first condition, at least the second injection is carried out in which the fuel is injected at a second timing later than the first timing in the compression stroke and at which the fuel goes toward the cavity.