A target cylinder (#3) is selected while an internal combustion engine (10) is operating in a steady state. The fuel injection quantity of the target cylinder (#3) is gradually increased or decreased and the fuel injection quantity of another cylinder (#1, #2, #4) is decreased or increased a corresponding amount in an inverse manner such that the overall air-fuel ratio of the internal combustion engine (10) does not change. During this time, the hydrogen content in exhaust gas is detected and the injection ratio when the hydrogen content is lowest is stored as an optimal injection ratio for each cylinder. Thereafter, fuel is injected into each cylinder at the optimal injection ratio for each cylinder.