A control device for an on-board compression-ignition engine in which partial compression-ignition combustion including spark ignition (SI) combustion performed by combusting a portion of mixture gas inside a cylinder by spark ignition followed by compression ignition (CI) combustion performed by causing the rest of the mixture gas inside the cylinder to self-ignite is executed within at least a part of an operating range of the engine, is provided. The device includes a detector configured to detect a parameter related to noise caused by the combustion inside the cylinder, and a combustion controller configured to control the combustion inside the cylinder during the partial compression-ignition combustion based on a combustion noise index value identified by the detected parameter of the detector and a given reference value defined as an upper limit of the combustion noise index value, the reference value increasing as a vehicle speed increases.