In this study, Typhoon Maysak (No. 09) in 2020 is numerically simulated using the WRF4.2, which replicates the transitional process and torrential rain caused by the gradual interaction of Maysak with the cold trough during its northward motion.The influence and mechanism of the cold trough on the spatial distribution and temporal variation of precipitation intensity are obtained by analyzing the thermodynamic, dynamical, and cloud microphysical characteristics of the typhoon"s eyewall and rainband areas. (1) The typhoon"s eyewall is invaded by dry and cold air from the middle atmosphere, which lowers the height of convection. The intrusion forms an unstable structure with a dry upper layer and a moist lower layer that favors the maintenance of convective intensity in the lower and middle atmosphere.In the rainband of typhoon, the importance of vertical vorticity transfer, as well as cold air invasion from lower atmosphere to lift warm air, enhances the upward motion of the middle and upper atmosphere. (2) The main cloud microphysical processes of this precipitation are as follows: the snow that comes from water vapor desublimation absorbs cloud water as it falls and melts into rainwater, which in turn collects a significant amount of cloud water, causing the rainwater to increase. There is also a part of rainwater originated from the melting of graupel and rainwater collected graupel , and graupel primarily produced by the process of cloud water collected by snow.(3) By changing the typhoon"s thermodynamic structure, the cold trough influences the spatial distribution of cloud water and snow, which in turn determines the spatial distribution of precipitation: Cloud water gathers toward the core in the eyewall , whereas snow is ahead of cloud water in the rainband along the direction of outflow. And rainwater is primarily distributed in areas where a certain amounts of snow and cloud water overlap.In terms of quantitative characteristics, the invasion of cold and dry air increases the efficiency of snow desublimation and rainwater evaporation in the rainband while decreasing the efficiency of cloud condensation, resulting in a higher proportion of snow and a lower proportion of cloud water and rainwater of the hydrometeors in the rainband. (4) The cold trough directly affects the efficiency of snow desublimation and cloud water condensation by changing the vertical velocity of the typhoon, which then tends to affect the efficiency of the processes of snow collecting cloud water, snow collecting cloud water converted into graupel, snow melting to rainwater, rainwater collecting cloud water, graupel melting to rainwater, and finally leads to the change of precipitation.