The hole transport capability of Ge1−xSnx alloys under the uniaxial compressive strain is comprehensively investigated by calculations using the nonlocal empirical pseudopotential method. The results indicate that the [110] uniaxial compressive strain is favorable for the hole transport of Ge1−xSnx alloys. For the [110] uniaxial compression, the strain-parallel hole effective mass of the top most valance band is the smallest, and the corresponding valance band splitting energy is the largest compared with the [100] uniaxial and the (001) biaxial compressive strain. In addition, the large uniaxial compressive strain and the high Sn composition are both beneficial for boosting the hole mobility of strained Ge1−xSnx alloys. The enhanced hole transport capability can be achieved through the [110] uniaxial compressive strain for high-performance Ge1−xSnx pMOSFETs applications.