A warm-up system for an exhaust system of an internal combustion engine includes an electronic control unit that performs warm-up control for warming up an exhaust system component upon start-up of the internal combustion engine and a failure diagnosis performing module of the electronic control unit that performs failure diagnosis for the exhaust system component after the completion of warm-up of the exhaust system component. If the internal combustion engine repeatedly stops before completion of the failure diagnosis for a predetermined period of time, then the electronic control unit changes the warm-up control performed upon start-up of the internal combustion engine to a control that raises the temperature of the exhaust system component more quickly than the warm-up control performed during the predetermined period.