An internal combustion engine includes a filter, which is configured to trap particulate matter in exhaust gas, an EGR passage, which connects a section of an exhaust passage that is upstream of the filter to an intake passage, and an EGR valve, which is configured to adjust a cross-sectional flow area of the EGR passage. A controller for the internal combustion engine includes processing circuitry, which is configured to execute a limiting process of limiting an opening degree of the EGR valve such that the opening degree is likely to decrease when an amount of the particulate matter trapped by the filter is great as compared to when the amount is small.