Starting device and compression ignition engine starting method

When the state of the compression ignition engine is automatically stopped, while performing fuel cut to stop the fuel injection valve (15) injects fuel, an intake throttle valve (30) in the operating position is set to be fully closed, and fully closed at least the maintained until the last TDC. Further, the fitting (32) is carried out after the fuel cut operation is controlled to adjust the engine load, so that when the engine speed after the final TDC (Net) falls within the (P) a predetermined range of a particular speed. Accordingly, the compression stop cylinder (2C) of the piston (5) with high precision at a target stop position, thereby reducing the time of restarting the engine, the target position is set between a top dead center and the bottom dead center position of the intermediate (CAx ) the bottom dead center side.