A controller executes an advancement process for advancing an injection start timing by a direct injection valve to a larger extent when a coolant temperature that is a temperature of coolant in an internal combustion engine is greater than or equal to a preset temperature than when the coolant temperature is lower than the preset temperature. The advancement process includes a retardation process for setting a smaller advancement amount at the injection start timing when a lubricant temperature that is a temperature of lubricant is lower than a predetermined temperature than when the lubricant temperature is greater than or equal to the predetermined temperature.