An exhaust passage of an internal combustion engine is provided with an upstream side three-way catalyst capable of purifying exhaust gas and a particulate filter (PM filter) for trapping particulate matter PM contained in exhaust gas. Catalyst warm-up control is exercised for the purpose of warming up mainly the upstream side three-way catalyst at cold start. Filter regeneration control for removing the particulate matter PM accumulating on the particulate filter from the filter is exercised at the cold start after the catalyst warm-up control is exercised.