Based on daily precipitation observation data at 120 national meteorological stations in Shandong Province, monthly reanalysis data of ERA-Interim from ECMWF (European Centre for Medium-Range Weather Forecasts) and 6-hour reanalysis data from NCEP/NCAR (National Centers for Environmental Prediction/National Center for Atmospheric Research) from 1979 to 2018, the influence of spring atmospheric heat source intensity over the Tibetan Plateau on summer rainstorm in Shandong Province was analyzed. The results show that rainstorm days presented an increasing trend in most areas of Shandong Province from 1979 to 2018, and the increasing trend of rainstorm days was significant in southwestern Shandong and the mid-east part of northwestern Shandong. The atmospheric heat source over the Tibetan Plateau was stronger than that in other areas of East Asia in spring and summer. The intensity of spring atmospheric heat source in strong central region over the Tibetan Plateau was significantly and positively correlated with summer rainstorm index in Shandong. When the atmospheric heat source over the Tibetan Plateau strengthened in spring, the South Asia high enhanced and extended to eastward in summer, and it was easily to appear “the central pattern” at 200 hPa. At the same time, the cold vortex at 500 hPa over northeastern China was easily to generate and moved southward, and the west Pacific subtropical high over eastern Japan strengthened and moved northward, the cold and warm airflow intersected over Shandong. In additional, there was significant water vapor transporting to Shandong from south to north. The circulation configuration with low-level convergence and upper-level divergence prompted updraft enhancement over Shandong, which was beneficial to rainfall. The intensity of atmospheric heat source over the Tibetan Plateau in spring had significantly positive and negative correlation with the South Asia high intensity and the Silk Road teleconnection correlation in summer, respectively, and the circulation situation under atmospheric heat source enhancement was conducive to occurrence of heavy rainfall in Shandong.