When starting an internal combustion engine from cold, after-burning of unburned HC in the exhaust gas within an exhaust passage is promoted by supplying secondary air into the exhaust passage upstream of a catalyst. At this time, the pressure within the exhaust passage is controlled by controlling the opening timing of an exhaust valve. Desirably, when the exhaust temperature has been elevated to a temperature at which it is possible to promote after-burning of the unburned HC in the exhaust gas within the exhaust passage, the opening timing of the exhaust valve is retarded.