Refractory high-entropy alloys (RHEAs) Al20+xCr20-xMo20-yTi20V20+y ((x, y) = (0, 0), (0, 10), and (10, 15)) were computationally studied to obtain a low density and a better mechanical property. The density functional theory (DFT) method was employed to compute the structural and mechanical properties of the alloys, based on a large unit cell model of randomly distributed elements. Debye–Grüneisen theory was used to study the thermal properties of Al20+xCr20-xMo20-yTi20V20+y. The phase diagram calculation shows that all three RHEAs have a single body-centered cubic (BCC) structure at high temperatures ranging from 1000 K to 2000 K. The RHEA Al30Cr10Mo5Ti20V35 has shown a low density of 5.16 g/cm3 and a hardness of 5.56 GPa. The studied RHEAs could be potential candidates for high-temperature application materials where high hardness, ductility, and low density are required.