For the first time, the damping behavior of high-entropy alloys was studied using the dynamic-mechanical analyzer, over a continuous heating temperature from room temperature to 773 K, at a given frequency range from 1 to 16 Hz in model alloys AlxCoCrFeNi (x = 0, 0.25, 0.5, 0.75, and 1). The experimental results reveal that the Al-rich alloys have a much smaller elastic storage- modulus amplitude over the temperature and thus a larger resistance to structural relaxation, while the Al-free and Al-lean alloys exhibit a much higher loss tangent and thus a much higher damping capability. Overall the elastic storage modulus decreases while the loss tangent increases with increasing the temperature, but little dependence was observed for the frequency. Several visible internal-friction peaks were presented in the face-centered cubic alloys, whose positions and heights are independent of the frequency. The damping capability of these alloys can be comparable to or even overwhelm the conventional Fe-Al alloys. The damping behavior above was proposed to be agreeable with the level of ordering (eta) of alloys characterized by two proposed parameters (the relative-entropy effect, Omega, and the atomic-size difference, delta).