Urea water is added to a catalyst in an exhaust pipe for purification. A first-order lag response model corresponding to the exhaust temperature upstream of the catalyst estimates catalyst temperature for each of divided cells of the catalyst. Cell volumes for each of temperature zones are summed on the basis of the estimated temperatures for the cells. The summation for each temperature zone is divided by the whole catalyst volume to determine temperature distribution volume ratio. The ratio for each of the temperature zones is multiplied by a reference injection amount of the urea water determined in consideration to a current engine operation status on the assumption that the catalyst temperatures are all within the temperature zone. The calculated values for the respective temperature zone are summed into a directive injection amount of the urea water.