To prevent a supply quantity of a reducing agent from becoming excessive, when intermittently supplying the reducing agent to a selective reduction type NOx catalyst in a short period.

A volume speed of exhaust gas supplied to the NOx catalyst is detected or estimated, and a duty period T in duty control of a reducing agent supply valve is changed in response to this detected or estimated volume speed. The duty period is lengthened in response to an increase in an exhaust volume speed (T2), and valve closing time of the reducing agent supply valve, that is, reducing agent supply stopping time is lengthened (T2-t2). Time required for a series of reduction reaction can be sufficiently secured, and excessive supply of the reducing agent can be prevented.