A start control device includes a compression self-ignition engine, fuel injection valve, piston stop position detector, starter motor, and controller for stopping the engine when an automatic stop condition is satisfied, and thereafter, when a restart condition is satisfied and a compression-stroke-in-stop cylinder piston stop position is within a stop position range on a bottom dead center side, restarting the engine by injecting fuel into the compression-stroke-in-stop cylinder while applying torque to the engine. In restarting the engine, when the restart condition is not based on driver request, when the compression-stroke-in-stop cylinder piston stop position is within the stop position range, the controller restarts the engine, injecting fuel into an intake-stroke-in-stop cylinder on an intake stroke, when the cylinder reaches the compression stroke. When the restart condition is based on driver request, the controller restarts the engine, injecting fuel into the compression-stroke-in-stop cylinder.