A control device for a compression-ignition engine in which partial compression-ignition combustion including spark ignition (SI) combustion performed by combusting a portion of a mixture gas inside a cylinder by spark-ignition followed by compression ignition (CI) combustion performed by causing the remaining mixture gas to self-ignite is executed at least within a part of an engine operating range is provided, which includes a detector configured to detect a given parameter that changes as combustion progresses inside the cylinder, an A/F (air-fuel ratio) controller configured to change an air-fuel ratio of air to fuel introduced into the cylinder, and a combustion controller configured to determine combustion stability based on the detected parameter of the detector and control the A/F controller to reduce the air-fuel ratio when it is confirmed that during the partial compression-ignition combustion the combustion stability is low.