A start control device includes a compression self-ignition engine, fuel injectors, a piston stop position detector, a starter motor and a controller for automatically stopping the engine when a predetermined automatic stop condition is satisfied, and thereafter, when a predetermined restart condition is satisfied and a compression-stroke-in-stop cylinder piston stop position is within a reference stop position range set relatively on a bottom dead center side, restarting the engine by injecting the fuel into the compression-stroke-in-stop cylinder while applying the rotational force to the engine using the starter motor. In restarting the engine, when the fuel is injected in the compression-stroke-in-stop cylinder, the controller controls the fuel injector to perform a pre-injection before a main injection and increase a total injection amount of the fuel for the pre-injection as the stop position of the compression-stroke-in-stop cylinder piston is further on a top dead center side.