A new mechanism of neutron acceleration in the accelerated perfect crystal is proposed and studied experimentally. The effect arises due to the resonance energy dependence of the neutron refraction index in vicinity of the Bragg's energy. During the neutron time-of-flight through the accelerated crystal the relative neutron-crystal velocity will be changing (with the deviation from the exact Bragg condition) and so the refraction index and the velocity of outgoing neutron will change as well.