The exhaust emission control device of an internal combustion engine in which accurate temperature information on a catalyst disposed on the exhaust passage of the internal combustion engine is obtained. Effect emthc by a gas temperature at the entrance of the catalyst and a temperature ethuf[end] at the rear end of the catalyst is calculated (step 102). An estimated value ethco of an exist gas temperature is calculated by a weighted average of the entrance gas temperature and the temperature ethuf[end] at the rear end of the catalyst in consideration of the above effect emthc (step 104). A temperature correction coefficient ekthuf[x] at each portion of the catalyst is calculated as the function f(emthc) of the above effect emthc (step 108). An estimated value correction ecthuf[x] is calculated by multiplying the deviation between the estimated value ethco of an exist gas temperature and an actual exit gas temperature measurement by an temperature correction coefficient ekthuf[x] (step 110). The estimated value correction ecthuf[x] is added to an estimated catalyst temperature (step 114).