A catalyst (22) suitable for reduction of the NOx in an exhaust gas by ammonia in the presence of excess oxygen is arranged in the exhaust passage (18, 21) of an internal combustion engine. An aqueous urea solution is fed through a flow control valve (33) to the inside of the exhaust passage (21) upstream of the catalyst (22). When the temperature of the catalyst (22) is low, a large amount of the aqueous urea solution is fed to make the urea contained in the aqueous urea solution be stored in the catalyst (22). When the engine is accelerated and the temperature of the catalyst (22) rises, ammonia is released at a little at a time from the inside of the catalyst (22) and the NOx in the exhaust gas is reduced by the released ammonia.