We describe a mechanism of resonant electron acceleration by oblique high-amplitude whistler waves under conditions typical for the Earth radiation belts. We use statistics of spacecraft observations of whistlers in the Earth radiation belts to obtain the dependence of the angle h between the wave-normal and the background magnetic field on magnetic latitude k. According to this statistics, the angle h already approaches the resonance cone at k 15 and remains close to it up to k 30–40 on the dayside. The parallel component of the electrostatic field of whistler waves often increases around k 15 up to one hundred of mV/m. We show that due to this increase of the electric field, the whistler waves can trap electrons into the potential well via wave particle resonant interaction corresponding to Landau resonance. Trapped electrons then move with the wave to higher latitudes where they escape from the resonance. Strong acceleration is favored by adiabatic invariance along the increasing magnetic field, which continuously transfers the parallel energy gained to perpendicular energy, allowing resonance to be reached and maintained. The concomitant increase of the wave phase velocity allows for even stronger relative acceleration at low energy <50 keV. Each trapping-escape event of electrons of 10 keV to 100 keV results in an energy gain of up to 100 keV in the inhomogeneous magnetic field of the Earth dipole. For electrons with initial energy below 100 keV, such rapid acceleration should hasten their drop into the loss-cone and their precipitation into the atmosphere. We discuss the role of the considered mechanism in the eventual formation of a trapped distribution of relativistic electrons for initial energies larger than 100 keV and in microbursts precipitations of lower energy particles.