TiZrTaNb-based high-entropy alloys (HEAs) are research frontier of biomedical materials due to their high hardness, good yield strength, excellent wear resistance and corrosion resistance. Sn, as an essential trace element in the human body that plays a significant role in physiological process. It has stable chemical properties and a low elastic modulus. In this study, a new material, TiZrTaNbSn HEAs, was proposed as a potential biomedical alloy. The Ti35Zr25Ta15Nb15Sn10 biomedical high-entropy alloys (BHEAs) were successfully prepared through an arc melting furnace and then remelted using a German high-temperature and high-pressure apparatus under GPa-level (4 GPa and 7 GPa). The precipitation behavior of the needle-like HCP-Zr5Sn3 phase that precipitates discontinuously at the grain boundary was successfully controlled. The phase constitution, microstructure, and corrosion resistance of the alloy were studied. The results show that the needle-like HCP-Zr5Sn3 phase is eliminated and the (Zr, Sn)-rich nano-precipitated phase is precipitated in the microstructure under high pressure, which leads to the narrowing of grain boundaries and consequently improves the corrosion resistance of the alloy. In addition, the formation mechanisms of (Zr, Sn)-rich nanoprecipitates in BHEAs were discussed. More Zr and Sn dissolve in the matrix due to the effect of high pressure, during the cooling process, they precipitate to form a (Zr, Sn)-rich nano-precipitated phase.