The disclosure provides a control device of a spark-ignition gasoline engine. When an operating state of an engine body is within a low engine speed range, a controller controls a fuel pressure variable mechanism so that a fuel pressure is higher within a high engine load range compared to a low engine load range, the controller operates, within the high engine load range, a fuel injection valve to perform a fuel injection at least at a timing that is more retarded than an injection timing of a fuel within the low engine load range and is within a retard period from a late stage of a compression stroke to an early stage of an expansion stroke, and the controller operates, within the high engine load range, an ignition plug to ignite at a timing within the retard period and further after the fuel injection.