When an internal combustion engine controller determines that an internal combustion engine is experiencing difficulty in starting, the fuel injection amount is corrected according to a first estimated ethanol (alcohol) concentration value that is approximately in the middle concentration value between the alcohol concentration of the fuel with the highest alcohol concentration and the alcohol concentration of the fuel with the lowest alcohol concentration among the fuels that can possibly be purchased in the market. If it is determined that the engine is experiencing difficulty in starting using the corrected fuel injection amount, the fuel injection amount is corrected a second time using a second estimated alcohol concentration value different from the first estimated alcohol concentration value. As a result, the engine air-fuel ratio can be optimized when starting the engine, so that poor engine starting can be quickly overcome.