Taking into account moisture in virtue of general potential temperature, the author derive a 3D pseudomomentum wave-activity relation for the moist atmosphere from the primitive equations in Cartesian coordinates using the Momentum-Casimir method. Since the wave-activity relation is constructed in an ageostrophic and non-hydrostatic dynamical framework, it may be applicable to diagnosing the evolution and propagation of mesoscale systems leading to heavy rainfall. The theoretical analysis shows that, besides the local change of wave-activity flux divergence and source or sink, the wave-activity relation includes two additional forcing terms. The first is the zonal gradient of difference between general potential temperature and potential temperature perturbations, and the second is the covariance of the solenoid and gradient of water vapor, denoting the direct influence of moisture on wave-activity density. The wave-activity density was applied to a heavy precipitation event occurring in the Jianghuai region of China. The calculation showed that the wave-activity density was consistent with 6-h accumulated precipitation observations, in terms of both spatial distribution and temporal tendency. This suggested that the disturbance represented by wave-activity density was closely related to the heavy precipitation. Although the wave-activity flux divergence and the covariance of the solenoid and gradient of water vapor made the primary contribution to the local change of wave-activity density, the covariance was more remarkable. The zonal gradient of difference between general potential temperature and potential temperature perturbations made a weaker contribution to the wave-activity density.