The moisture sources of precipitation in the Tianshan Mountains, one of the regions with the highest precipitation in Central Asia during 1979-2017 are comprehensively and quantitatively summarized by using a Lagrangian moisture source detection technique. Continental sources provide about 93.2\% of the moisture for precipitation in the Tianshan Mountain, while moisture directly from the ocean is very limited, averaging only 6.8\%. Central Asia plays a dominant role in providing moisture for all sub-regions of the Tianshan Mountains. For the Western Tianshan, moisture from April to October comes mainly from Central Asia (41.4\%), while moisture from November to March is derived primarily from Western Asia (45.7\%). Nearly 13.0\% of moisture to precipitation for Eastern Tianshan in summer originates from East and South Asia, and the Siberia region. There is a significant decreasing trend in the moisture contribution of local evaporation and Central Asia in the Eastern Tianshan during winter. The contribution of moisture from Europe to summer precipitation in the Central and Eastern Tianshan and the contribution of the North Atlantic Ocean to summer precipitation in the Northern, Central, and Eastern Tianshan also exhibit a decreasing trend. The largest increase in moisture in Western Tianshan stems from West Asia during extreme winter precipitation months. Europe is also an important contributor to extreme precipitation in the Northern Tianshan. The moisture from East and South Asia and Siberia during extreme precipitation months in both winter and summer is significantly enhanced in the Eastern Tianshan.