A control device of a spark-ignition engine is provided. The control device includes a main body of the engine, a fuel injection valve, an ignition plug, and a controller. According to an engine operating state, the controller switches between a compression-ignition mode in which compression-ignition combustion is performed, and a spark-ignition mode in which spark-ignition combustion is performed. The controller switches from the spark-ignition mode to the compression-ignition mode by performing in order, a first stage where an air-fuel ratio of mixture gas is set to a predetermined value and the spark-ignition combustion is performed, a second stage where the air-fuel ratio of the mixture gas is set leaner than the first stage and the compression-ignition combustion is performed, and a third stage where the air-fuel ratio of the mixture gas is set richer than the second stage and the compression-ignition combustion is performed.