A competence diagnosis system for a urea water temperature sensor that can limit a diagnosis during a cold start. The system includes a cold start condition determination unit that obtains a difference between an engine cooling water temperature and an ambient temperature, a difference between an engine cooling water temperature and a fuel temperature, and a difference between an ambient temperature and a fuel temperature by using an engine cooling water temperature, an ambient temperature, and a fuel temperature measured immediately after engine starting, and allows a diagnosis by the competence diagnosis unit when the temperature differences are less than or equal to a predetermined threshold value.