A secondary-air supply system for an internal combustion engine, including a catalyst provided in an exhaust passage and configured to purify exhaust gas from the engine, and a secondary-air supply source and a secondary-air valve provided in a secondary-air passage connected upstream from the catalyst. A secondary-air supply device is configured to drive the secondary-air supply source and to open the secondary-air valve to supply secondary air to the exhaust passage upstream from the catalyst under a warm-up condition of the engine. Secondary-air supply control means is configured to control the secondary-air supply device to drive the secondary-air supply source and to open the secondary-air valve under a high-load operating condition where a flow rate of the exhaust gas is high, the high-load operating condition being different from the warm-up condition.