To improve emission for early warm-up of catalyst by reducing unburned HC from an internal combustion engine during secondary air supply including the initial stage of the secondary air supply.

When increasing the fuel injection amount to the internal combustion engine so as to maintain the air-fuel ratio (A/F) before catalyst introduced to a three-way catalyst, which is detected by an A/F sensor during secondary air supply by a secondary air supply mechanism, a prescribed delay time from the start of the secondary air supply is set for the increased amount (time t1 to t2 in Fig.(a)), and the fuel injection amount based on the air-fuel ratio supplied to the internal combustion engine to contribute to the combustion is gradually changed until it reaches a BASE value, which is the increased amount (time t2 to t3 of Fig.(a)). This allows reduction of the unburned HC from the internal combustion engine that accompanies the incremental compensation in the fuel injection amount to the internal combustion engine during the secondary air supply including the initial stage of the secondary air supply. Accordingly, the early warm-up of the catalyst can be realized while improving emission control.