  In this paper, using Hamilton-Jacobi method, we address the tunnelling of
fermions in a 4-dimensional Schwarzschild spacetime. Base on the generalized
uncertainty principle, we introduce the influence of quantum gravity. After
solving the equation of motion of the spin 1/2 field, we derive the corrected
Hawking temperature. It turns out that the correction depends not only on the
black hole's mass but also on the mass (energy) of emitted fermions. It is of
interest that, in our calculation, the quantum gravity correction decelerates
the temperature increase during the radiation explicitly. This observation then
naturally leads to the remnants in black hole evaporation. Our calculation
shows that the residue mass is $\gtrsim M_p/\beta_0$, where $M_p$ is the Planck
mass and $\beta_0$ is a dimensionless parameter accounting for quantum gravity
effects. The evaporation singularity is then avoided.
