Abstract: The moist jet stream is a scientific imagination supposed by Y. B. Xie (i.e. Y. P. Hsieh) based on his long time research work of precipitation of China and animated by the static energetic method of heavy rainfall prediction supposed by Y. S. Lei. In recent year, a couple of meso-scale numerical simulations of heavy rainfall support the presence of the moist jet stream, which links the low level jet and the upper level jet in the heavy rainfall region. Using the modern visualization technology, trajectories of moist air parcels rising, acceleration and turning could be displayed on the computer screen. But,the calculation of momentum budget shows that the increasing of momentum caused not only by the buoyancy force, but also by the horizontal pressure gradient force on mesoscale.The moist baroclinic balance equation (i.e. moist thermal wind equation) was discussed, which indicated that the total energy conservation can not reveal the conversions between different energy forms. Since the process of heavy rainfall is highly nongeostrophic balance, also non-hydrostatic balance, and being multi-scale interactions, the numerical model with with fine resolution and complete physic processes is the most powerful tool for heavy rainfall research.