To provide a controller that can slow down progression of deterioration of an internal combustion engine caused by repeated occurrence of LSPI. An index value of the degree of deterioration of the internal combustion engine caused by LSPI is calculated. If the index value exceeds a first threshold, when the temperature of cooling water that cools a part of the peripheral wall of a cylinder that is close to a combustion chamber is lower than a threshold temperature, and the internal combustion engine is running in a determined operational region set in a low speed and high load region, the proportion of fuel injection by an in-cylinder injection valve is reduced to increase the proportion of fuel injection by a port injection valve compared with before the index value exceeds the first threshold, thereby suppressing occurrence of LSPI.