Fuel injection control for start-up of internal combustion engine

An internal combustion engine (2) provided with a starter motor sequentially performs combustion of fuel in a plurality of cylinders (#1 - #4). Each cylinder is provided with an intake port (7) and a fuel injector (8) to inject fuel in the intake port (7) and repeatedly performs an intake stroke, compression stroke, expansion stroke and an exhaust stroke. A sensor (9, 11) generates a signal identifying a cylinder in a specific position in a specific stroke and the controller (1) executes a cylinder-stroke identification in response to the signal. Upon the first execution of the cylinder-stroke identification when the engine is cranked, a fuel injection is performed for a cylinder in the intake stroke and for a cylinder in the exhaust stroke simultaneously so as to ensure the fuel supply amount required for the first combustion in each cylinder.