This control device of a compression autoignition engine is provided with an engine (1), a state quantity setting device (23, 24, 43, 48, 54), an injector (6), a spark plug (25), a controller (ECU10), and sensors (SW1-SW16). When the operation state of the engine is in a prescribed operation region, the controller sets the state in the combustion chamber (17) such that G/F is 18.5-30 and the excess air ratio λ is 1.0±0.2. The spark plug ignites the air-fuel mixture at a prescribed timing such that the ignited air-fuel mixture combusts through flame propagation and, thereafter, the unburned air-fuel mixture combusts through autoignition.