The Mesozoic and Cenozoic tectonic magmatic activity in the Lhasa block has always been one of the research hotspots in the basic geology of the Qinghai-Xizang Plateau. There are many Cenozoic, especially Miocene magmatic rocks developed in the western part of the Lhasa block. This article takes the newly discovered Miocene granite in the Anglonggangri area of the western Lhasa block as the research object, and explores its rock types, rock genesis, and tectonic background. The Miocene granites in the Anglonggangri area are composed of fine-grained muscovite monzonitic granite and medium-fine-grained monzonitic granite, with a small amount of dark inclusions developed internally. The zircon U-Pb age of fine-grained muscovite monzonitic granite is 9.95±0.14 Ma, and the zircon U-Pb age of medium-fine-grained monzonitic granite is 10.68±0.2 Ma, both from the Miocene. Both of them have the characteristics of high silicon (SiO₂=72.35%~74.74%), rich potassium (K₂O/Na₂O=1.15~1.45, all greater than 1), high aluminum (Al₂O₃=14. 35%~14.83%), and weak peraluminum peraluminum (A/CNK=1.08~1.14). The number of CIPW corundum molecules is greater than 1%. The differentiation of light and heavy rare earth elements is very obvious, with a moderate negative Eu anomaly, enriched in large ion lithophile elements such as Rb, Th, K, and depleted in high field strength elements such as Nb, relatively enriched in high field strength elements such as Hf and Zr, Sr, Ba, P, Ti, etc. These characteristics indicate that it is a high potassium calcium alkaline series of peraluminous S-type granite. Both of them have relatively low Sr, high Sr/Y, La/Yb ratios, and extremely low Y and Yb contents. The granite in the research area originated from a thickened lower crustal environment and underwent a certain degree of magma mixing. Based on the comprehensive regional research results, the formation of Miocene granites in the Anglonggangri area may be related to the northward subduction of the Indian plate into the north Lhasa block, where plate tearing occurred and high-temperature asthenosphere material flowed through the plate fragments, causing partial melting of the lower crust.