The transient process of establishing the electron current in a vacuum diode is theoretically investigated, in which the kinetic energies of electrons can exceed the amplitude value of the applied voltage (multiplied by the elementary charge). It is shown theoretically that when a high voltage pulse with a short leading edge is applied to a planar vacuum diode, the first peak of relaxation current oscillations is provided by an electron beam of “anomalously” high energies. It is noted that the degree of “abnormality” of electron beam energies significantly depends on the density of the emission current from the cathode, and in some hypothetical cases, it can exceed the applied voltage several times.