By using the monthly ERA-40 reanalysis data and observed rainfall data, we investigated the effect of the Indian summer monsoon (ISM) on the South Asian High (SAH) at 200 hPa, and the role played by the SAH in summer rainfall variation over China. It is found that in the interannual timescale the east-west shift is a prominent feature of the SAH, with its center either over the Iranian Plateau or over the Tibetan Plateau. When the ISM is stronger (weaker) than normal, the SAH shifts westward (eastward) to the Iranian Plateau (Tibetan Plateau). The east-west position of SAH has close relation to the summer rainfall over China. A westward (eastward) location of SAH corresponds to less (more) rainfall in the Yangtze-Huai River Valley and more (less) rainfall in North China and South China. A possible physical process that the ISM affects the summer rainfall over China via the SAH is proposed. A stronger (weaker) ISM associated with more (less) rainfall over India corresponds to more (less) condensation heat release and anomalous heating (cooling) in the upper troposphere over the northern Indian peninsula. The anomalous heating (cooling) stimulates positive (negative) height anomalies to its northwest and negative (positive) height anomalies to its northeast in the upper troposphere, causing a westward (eastward) shift of the SAH with its center over the Iranian Plateau (Tibetan Plateau). As a result, an anomalous cyclone (anticyclone) is formed over the eastern Tibetan Plateau and eastern China in the upper troposphere. The anomalous vertical motions in association with the circulation anomalies are responsible for the rainfall anomalies over China. Our present study reveals that the SAH may play an important role in the effect of ISM on the East Asian summer monsoon.