  Quantum gravity correction is truly important to study tunnelling process of
black hole. Base on the generalized uncertainty principle, we investigate the
influence of quantum gravity and the result tell us that the quantum gravity
correction accelerates the evaporation of black hole. Using corrected Dirac
equation in curved spacetime and Hamilton-Jacobi method, we address the
tunnelling of fermions in a 4-dimensional Schwarzschild spacetime.
  After solving the equation of motion of the spin 1/2 field, we obtain the
corrected Hawking temperature. It turns out that the correction depends not
only on the mass of black hole but aslo on the mass of emitted fermions. In our
calculation, the quantum gravity correction accelerates the increasing of
Hawking temperature during the radiation explicitly. This correction leads to
the increasing of the evaporation of black hole.
