The topological insulator/superconductor heterostructure is one of the most promising platforms to create and manipulate Majorana bound states. Here, we used molecular beam epitaxy to grow high-quality (Bi0.5Sb0.5)2Te3 films on Nb surfaces. To promote proper (Bi0.5Sb0.5)2Te3 film nucleation in the early growth stage, we developed a two-step growth method. Bi, Sb, and Te clusters were first evaporated at a low temperature of 180 °C, which is below the typical growth temperature and then annealed to form a crystalized passivation layer. Second, a standard (Bi0.5Sb0.5)2Te3 film was grown under the normal deposition temperature of 280 °C. We used reflection high-energy electron diffraction, high-resolution transmission electron microscopy, X-ray photoelectron spectroscopy, and X-ray diffraction to further characterize the (Bi0.5Sb0.5)2Te3 film and passivation layer quality. Finally, the top Nb film was laid down by magnetron sputtering at room temperature. The hetero-Nb/epitaxial (Bi0.5Sb0.5)2Te3/Nb stacks were further fabricated into micro-Josephson junctions and showed clear Josephson currents demonstrating an excellent material quality.