The superconducting transition temperature (<i>T</i><sub>c</sub>) 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 <i>T</i><sub>c</sub> 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 <i>T</i><sub>c</sub> 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)<sub>0.67</sub>(HfZrTi)<sub>0.33</sub> and (ScZrNbTa)<sub>0.6</sub>(RhPd)<sub>0.4</sub>, 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 <i>T</i><sub>c</sub> of conventional or unconventional superconductors.