We present a new particle acceleration mechanism called ultra-relativistic acceleration (URA). URA comprises electron energization due to a special form of nonlinear phase trapping by a coherent whistler-mode wave for electrons with an initial Lorentz factor gamma(0) satisfying gamma(0) > Omega(EQ)/omega; omega is the wave frequency and Omega(EQ) is the electron cyclotron frequency at the equator of an assumed dipole magnetic field. Radiation belt electrons that encounter a combination of relativistic turning acceleration (RTA) followed by multiple URA interactions can undergo significant energy increase. Under ideal conditions, at Earth (L = 4) several-hundred-keV electrons can be energized to several MeV within a few seconds, while at Jupiter (L = 8), several-hundred-keV electrons can be energized by tens of MeV in a few tens of seconds. URA can play a prominent role in generating the several- MeV electrons observed in Earth's outer zone and the tens-of-MeV electrons observed in Jupiter's magnetosphere. More generally, we expect URA to be an effective electron energization mechanism in cosmic plasma environments that contain a magnetic mirror geometry and electromagnetic whistler-mode emissions.