We have demonstrated high hole mobility in strained In0.25Ga0.75Sb quantum well (QW) structure with a high quality Al0.95Ga0.05Sb buffer layer for future single channel complementary metal-oxide-semiconductor circuits. The Al0.95Ga0.05Sb buffer layer is important to achieve low substrate leakage and guarantee good channel material quality and high hole mobility. We grew buffer layers with various Sb effective flux conditions using molecular beam epitaxy to obtain high crystal quality and proper electrical properties. We systematically evaluated the relationship between the crystal quality and electrical properties using X-ray diffraction, atomic force microscope, Raman, and the Hall effect measurement system. Then, on this optimized buffer layer, we grew the In0.2Al0.8Sb/In0.25Ga0.75Sb/linear-graded Al0.8Ga0.2Sb QW structure to obtain high hole mobility with compressive strain. Moreover, the compressive strain and hole mobility were measured by Raman and Hall effect measurement system. The results show a compressive strain value of 1.1% in In0.25Ga0.75Sb QW channel, which is very close to the theoretical value of 1.1% from lattice mismatch, exhibiting the highest hole mobility of 1170 cm2/V s among reported mobility in In0.25Ga0.75Sb QW. Furthermore, it was able to be fabricated as p-type Fin-FET and shown the excellent electrical characteristics with low Smin and high gm.