This paper uses the daily precipitation data of 756 observation stations from 1958 to 2013 provided by National Climate Center of China Meteorological Administration to define “weak typhoon heavy rainfall event” (WTHRE). The spatial-temporal distribution of the frequency of WTHRE is statistically analyzed and anomalous atmospheric circulation favorable for WTHRE is investigated as well. The results are listed as follows. 1) WTHRE occurs mostly from May to October, but its proportion in all precipitation events is the highest in October. 2) The number of WTHRE increases significantly after the mid-1980s, presenting a periodic oscillation of three to 5 years. The midsummer (from July to August) is the main period of WTHRE. 3) Spatially, the coverage area of WTHRE is the smallest in early summer (from May to June) and the biggest in midsummer. 4) The favorable atmospheric circulation for WTHRE is under the anomalous circulation background of the positive phase of Arctic Oscillation, therefore, the mid-latitude westerly is relatively stable and straight, which is in favor of a continuous stable stationary wave train of circum-global teleconnection pattern in the middle latitude causing the anomalous high in East Asia. The maintenance of anomalous high in East Asia, which is favorable for the southward of cold air, meets the warm and humid air brought by tropical cyclones to form precipitation. 5) At the same time, the weakening of the western Pacific subtropical high is beneficial to increase typhoon's duration of stay in China and sustain water vapor transport. The water vapor mainly comes from the tropical monsoon region such as the southwest side of the North Pacific, the South China Sea, and the Bay of Bengal.