Giant enhancement of the non-linear response of a single crystal of Nb placed in a sweeping magnetic field has been experimentally observed. The rectified signal from Nb (Tc = 9.15 K) has been measured by means of an inductive method as a function of temperature, dc field, dc field sweep rate, and the amplitude of ac field. The Nb sample was excited by an amplitude modulated ac field. Under a stationary regime, the rectified signal appears only for magnetic fields (H0) in the range Hc2 < H0 < Hc3. However, when the dc field was swept slowly, the rectified signal appears at H0 > Hc1. This experiment shows that the amplitude of the rectified signal is two orders of magnitude larger than the amplitude of the signal seen under stationary field conditions. Moreover, the amplitude of the rectified signal is a power function of the sweep rate, with the power exponent close to 1.