A system of diagnosing a deterioration of a catalyst, which includes a precious metal component and a ceramic part and purifies an exhaust gas emitted from an engine, includes: a diagnosis means comparing a diagnosis object value corresponding to an output from an NOx sensor provided on a downstream side with respect to the catalyst and a predetermined diagnosis threshold value stored in a storage means, thereby diagnosing a degree of deterioration of the catalyst, wherein the diagnosis threshold value is previously determined based on a correlationship between the diagnosis object value and a total weight value of NOx and THC in the exhaust gas through the catalyst in a state where the vehicle travels under a constant threshold value setting condition, and the diagnosis means diagnoses that a deterioration occurs in the precious metal component when the diagnosis object value exceeds the diagnosis threshold value.