  The Crab Pulsar has been recently detected at very high energies (VHE) with
its pulsed VHE emission reaching up to $1.5$ TeV. The VHE peaks appear
synchronised with the peaks at GeV energies and show VHE spectra following hard
power-law functions. These new findings have been interpreted as evidence for a
gamma-ray production that happens very close to the light cylinder. Motivated
by these experimental results we consider the efficiency of magnetocentrifugal
particle acceleration in the magnetosphere of the Crab Pulsar, reexamining and
extending results obtained in a previous work (Osmanov & Rieger 2009). It is
shown that efficient magnetocentrifugal acceleration close to the light
cylinder could provide the required electron Lorentz factors of $5\times 10^6$
and that the resulting inverse Compton (IC) scattering off thermal photons
might explain the enigmatic TeV emission of the pulsar. We estimate the
corresponding VHE luminosity and provide a derivation of its spectral
characteristics, that appear remarkably close to the observational results to
encourage further studies.
