An in-cylinder-injection internal combustion engine of spark ignition type has a plurality of cylinders, a fuel accumulator for storing a pressurized fuel; a fuel injector system that injects the pressurized fuel into each of the cylinders; a spark ignition system that ignites the fuel injected into each of the cylinders; and is controlled such that the engine is started by a partial operation of a selected at least one of the cylinders with a fuel injected into the selected at least one of the cylinders in at least its intake stroke. Then, a full operation of all of the cylinders with the fuel injected into all of the cylinders is started. The full operation is initiated not before a pressure of the fuel in the fuel accumulator has been raised to a level high enough to permit injection of the fuel into each of the cylinders in its compression stroke, as a result of the partial operation of the selected at least one of the cylinders. In addition, the engine is controlled such that an initial portion of the full operation includes a first mode of combustion in the selected at least one of the cylinders with the fuel injected thereinto in at least its intake stroke, the first mode of combustion being followed by stratified charge combustion in the selected at least one of the cylinders with the fuel injected thereinto in only its compression stroke.