Sulphur oxides in the exhaust gas of a vehicle engine (1) are trapped by a nitrogen oxide trapping catalyst (5A). A controller (6) calculates the sulphur oxide poisoning amount of the trapping catalyst (5A) from the running condition of the vehicle (S13), and desulphating the sulphur oxides by a removing mechanism (3, 4, 14). The release amount of sulphur oxides per unit time due to desulphating is set as a parameter based on the sulphur oxide poisoning amount (S11), and by integrating the calculated release amount using the parameter, the current poisoning amount is calculated, and the release completion timing is precisely found.