Abstract: Granite is the first choice for many important engineering foundations or surrounding rocks. A variety of granite samples from the Bayannuorigong granite mass in the Alxa pre-selected region for geological disposal of high-level nuclear waste were subjected to petrographic studies. The same samples were then tested to determine the uniaxial compressive strength. The relationships between the uniaxial compressive strength and the mineralogical characteristics are described by simple regression analyses. The results show that the influence of K-feldspar and biotite on the uniaxial compressive strength of the granite is obvious. However, the influence of plagioclase and quartz is not obvious. The correlation between the mineral grain size and the uniaxial compressive strength is not obvious, but it is obviously correlated for the rock with the same structure. The strength of granite depends not only on the mineral compositions and grain size, but also on the details of its internal structure (such as microcracks, mineral arrangement, cementation, etc.).