Isothermal oxidation behavior of a refractory high-entropy NbCrMo0.5Ta0.5TiZr alloy was studied during heating at 1273 K for 100 h in flowing air. Continuous weight gain occurred during oxidation, and the time dependence of the weight gain per unit surface area was described by a parabolic dependence with the time exponent n = 0.6. X-ray diffraction and scanning electron microscopy accompanied by energy-dispersive X-ray spectroscopy showed that the continuous oxide scale was made of complex oxides and only local (on the submicron levels) redistribution of the alloying elements occurred during oxidation. The alloy has a better combination of mechanical properties and oxidation resistance than commercial Nb alloys and earlier reported developmental Nb-Si-Al-Ti and Nb-Si-Mo alloys.