The quasi-geostrophic theory is the theoretical basis of the short-term weather forecast. Quasi-geostrophic motion equations of mid-latitude synoptic -scale movement are the core of quasi-geostrophic theory. Based on baroclinic two-layer model, quasi-geostrophic potential tendency equation and vertical motion equation can more clearly explain the movement and development of upper and surface weather systems. The movement of 500 hPa upper trough depends on the vorticity advection of 500 hPa, its development is determined by 500 hPa vorticity advection and differential vorticity advection between 250 and 750 hPa . The movement and development of cyclone depend on the positive temperature advection at 500 hPa and differential vorticity advection between 250 and 750 hPa. A case of snoptic system evolution demonstrates that quasi-geostrophic theory based on baroclinic two-layer model is conducive to the quick recognition of the characteristics of mid-latitude synoptic scale baroclinic development system, the understanding of the objective law of the development of the weather systems and the physical basis of numerical products.