An exhaust passage (15) of an internal-combustion engine (10) includes a selective reduction NOx catalyst (34) and an after-catalyst NOx sensor (50) for detecting a NOx concentration Cr at the downstream thereof. Reducing agent is selectively added from an addition valve (40) to the NOx catalyst. A NOx concentration Ce at the upstream side of the NOx catalyst is detected or estimated. NOx concentrations Cr and Ce before and after the NOx catalyst, which were detected or estimated during the stoppage of an addition of the reducing agent, are compared to each other to thereby determine an abnormality of the after-catalyst NOx sensor (50). An abnormality diagnosis is executed while the addition of reducing agent is being stopped to remove an influence by the NOx catalyst.