Abstract: The introduction of generalized potential temperature and tendency equation of generalized moist potential vorticity into the thermodynamic framework is based on the non-uniform saturation of real atmosphere. The generalized moist potential vorticity (GMPV) equation is deduced by absorbing the generalized potential temperature. The water vapor and its gradient effect can be manifested in the GMPV equation, which indicates the convergence mechanism of water vapor at lower levels when torrential rain occurs. The GMPV anomaly is used in diagnostic studies of torrential rain both in North China and Yangtze River Basin. The results show that dynamic identification and forecasting of torrential rain from the perspective of generalized moist potential vorticity and its anomaly are effective, which maybe provide a new thought for the operational application of the GMPV.