A control device for a compression self-ignition engine including a cylinder, a piston fitted in the cylinder and having a concave cavity formed in a crown surface thereof, and an intake valve configured to open and/or close an intake port configured to introduce intake air into a combustion chamber defined by the cylinder and the piston, the engine being configured to execute compression self-ignition combustion in which a mixture gas of fuel and air combusts inside the combustion chamber by self-ignition, the control device comprising: a fuel injection system configured to inject fuel from a ceiling surface of the combustion chamber into the combustion chamber; and an injection controller configured to cause the fuel injection system to carry out a first injection to inject fuel at a first timing (t_F2) in a compression stroke, and a second injection to inject fuel at a second timing (t_F3) later than the first timing (t_F2) in the compression stroke, thereby executing the compression self-ignition combustion, wherein the fuel injection system is configured to inject fuel at the first timing (t_F2) toward a part radially outward of the cavity, and the fuel injection system is configured to inject fuel at the second timing (t_F3) toward the cavity, the injection controller is configured to cause the fuel injection system to carry out the first injection and suspend the second injection, thereby operating the engine by the compression self-ignition combustion under a given first condition, and the injection controller is configured to cause the fuel injection system to carry out at least the second injection, thereby operating the engine by the compression self-ignition combustion under a second condition in which a temperature inside the combustion chamber at a close timing of the intake valve is lower than the temperature under the first condition, characterized in that the injection controller is configured to estimate an in-cylinder temperature inside the combustion chamber at a close timing of the intake valve, and the injection controller is configured to determine a first injection amount that is an amount of fuel injected at the first timing (t_F2) and a second injection amount that is an amount of fuel injected at the second timing (t_F3) based on the estimated in-cylinder temperature. a fuel injection system configured to inject fuel from a ceiling surface of the combustion chamber into the combustion chamber; and an injection controller configured to cause the fuel injection system to carry out a first injection to inject fuel at a first timing (t_F2) in a compression stroke, and a second injection to inject fuel at a second timing (t_F3) later than the first timing (t_F2) in the compression stroke, thereby executing the compression self-ignition combustion, wherein the fuel injection system is configured to inject fuel at the first timing (t_F2) toward a part radially outward of the cavity, and the fuel injection system is configured to inject fuel at the second timing (t_F3) toward the cavity, the injection controller is configured to cause the fuel injection system to carry out the first injection and suspend the second injection, thereby operating the engine by the compression self-ignition combustion under a given first condition, and the injection controller is configured to cause the fuel injection system to carry out at least the second injection, thereby operating the engine by the compression self-ignition combustion under a second condition in which a temperature inside the combustion chamber at a close timing of the intake valve is lower than the temperature under the first condition, characterized in that the injection controller is configured to estimate an in-cylinder temperature inside the combustion chamber at a close timing of the intake valve, and the injection controller is configured to determine a first injection amount that is an amount of fuel injected at the first timing (t_F2) and a second injection amount that is an amount of fuel injected at the second timing (t_F3) based on the estimated in-cylinder temperature.