The superconducting transition temperature (T_c) of superconductor is related intimately to multiple degree of freedom of charge, spin, orbital and lattice. Many studies have indicated that pressure is an effective way to tune T_c though changing crystal structure and electronic structure. Here, we report a new progress made in the high-pressure studies – discovery of a new type of superconductors whose T_c is robust against large volume shrinkage under extremely high pressure, named RSAVS (robust superconductivity against volume shrinkage) superconductor. Such RSAVS behavior was observed initially in the high entropy alloys of (TaNb)_0.67(HfZrTi)_0.33 and (ScZrNbTa)_0.6(RhPd)_0.4, then in the widely-used NbTi alloy, Nb and Ta elements. Analysis shows that this type of superconductor possesses a body-centered cubic crystal structure and is composed of transition metal elements. The observed results not only present new research topics but also raise the question of what determines T_c of conventional or unconventional superconductors.