The phase, local lattice distortions, elastic and mechanical properties of a novel NbHfTaW refractory high-entropy alloy (RHEA) have been investigated via theoretical calculations and experiments. The single body-centered cubic (BCC) structure of the RHEA has been predicted by CALPHAD and examined by XRD. The first-principle calculations indicate a severe local lattice distortions (LLD) in NbHfTaW. Meanwhile, the alloy shows a fascinating elastic isotropy feature that would be favorable for its engineering applications. The electronic structure of the alloy suggests an inhomogeneous strong bonding near Hf atoms. NbHfTaW also shows good comprehensive mechanical properties, with an ultimate strength of 2.31 GPa and a compressive strain of 18.2%.