A typical mesoscale convective system (MCS) over the second-step terrain that moved eastward, merged with convection moving eastward from the eastern edge of the Tibetan Plateau (TP), and influenced the downstream convection systems, had been studied using a numerical simulation. The case occurred from June 29 to July 1, 2016, and resulted in heavy precipitation in the middle reaches of the Yangtze River to the Yangtze-Huai River Basin. This simulation had successfully reproduced the eastward movement of the MCSs over the second-step terrain and the merging with convection moving eastward from the TP, which affected the downstream convective systems. The results revealed the spatiotemporal distribution of precipitation over the middle and lower Yangtze River. The evolution of the MCS is divided into four stages: the formation stage, the propagation stage, the merging stage, and the weakening stage. Due to the cyclonic disturbance in the northeastern part of the Southwest Vortex, the MCS formed in the western mountainous area over the second-step terrain. After moving eastward out of the second-step terrain, the MCS merged with the eastward-propagating convection from the eastern edge of the TP over the downstream areas, which promoted the strong development of upward motion, enhanced the convergence in the lower layers, and induced a mesoscale vortex in the lower troposphere. The mesoscale vortex and the merged convection gradually coupled, triggering heavy rainfall in the eastern plains east of the second-step terrain.