Catalyst control apparatus for internal combustion engine and method for performing catalyst control

A degree of deviation between an actual air-fuel ratio and a value detected by an air-fuel ratio sensor is obtained as a difference dTHC between a target catalyst bed temperature THCt and a catalyst bed temperature THC (S118). The difference dTHC is converted to a target air-fuel ratio correction amount daft according to a target air-fuel ratio correction amount map Mapaft (S120). A target air-fuel ratio AFt is corrected using the target air-fuel ratio correction amount daft (S122), whereby the degree of deviation between the actual air-fuel ratio and the value detected by the air-fuel ratio sensor is reflected in an air-fuel ratio feedback control. Thus, even if there is a difference between the actual air-fuel ratio and a detected air-fuel ratio AF, the air-fuel ratio feedback control can be appropriately performed, and a catalyst control can be appropriately performed. Accordingly, it is possible to prevent a situation in which the catalyst cannot sufficiently recover from sulfur poisoning, or a situation in which smoke and hydrogen sulfide (H2S) are discharged.