The acceleration of an electron by the ponderomotive force of a Gaussian whistler pulse in a magnetized high-density quantum plasma obeying Fermi–Dirac distribution is studied using the recently developed quantum hydrodynamic model. Effective acceleration takes place when the peak whistler amplitude exceeds a threshold value, and the whistler frequency is greater than the cyclotron frequency. The threshold amplitude decreases with ratio of plasma frequency to electron cyclotron frequency. The electron is accelerated at velocities of about twice the group velocity of the whistler.