By using the NCEP/NCAR daily reanalysis data from 1948 to 2013, the establishment or retreatment average date of South Asian High (SAH) over the Tibetan Plateau and its relation with the Tibetan Plateau summer monsoon onset was analyzed. Results show that the SAH moved northward at the beginning of April, jumpped northward abruptly in May, reached to the most northern position of 55°N in August, and then withdrew southward in September. SAH moved westerly stablely from May to October, and swang drastically from November to the next April. It is concluded that the first establishment average date of SAH over the Tibetan Plateau is on the 33rd pentad of June,and the climate-mean SAH moving out over the Tibetan Plateau is on the 58th pentad of October. The moving date of SAH on the Tibetan Plateau is 73 days later than that of the Plateau summer monsoon onset, and the retreatment date over the Tibetan Plateau is 5 days earlier than that of the plateau winter monsoon onset. The relation between establishment of SAH over the Tibetan Plateau and Tibetan Plateau summer monsoon onset can be explained the thermal effects of the Tibetan Plateau at different stages, which depend on different heights.