  In this paper, we have applied the Lorentz-invariance-violation (LIV) class
of dispersion relations (DR) with the dimensionless parameter n = 2 and the
"sign of LIV" {\eta}_+ = 1, to phenomenologically study the effect of quantum
gravity in the strong gravitational field. Specifically, we have studied the
effect of the LIV-DR induced quantum gravity on the Schwarzschild black hole
thermodynamics. The result shows that the effect of the LIV-DR induced quantum
gravity speeds up the black hole evaporation, and its corresponding black hole
entropy undergoes a leading logarithmic correction to the "reduced
Bekenstein-Hawking entropy", and the ill defined situations (i.e. the
singularity problem and the critical problem) are naturally bypassed when the
LIV-DR effect is present. Also, to put our results in a proper perspective, we
have compared with the earlier findings by another quantum gravity candidate,
i.e. the generalized uncertainty principle (GUP). Finally, we conclude from the
inert remnants at the final stage of the black hole evaporation that, the GUP
as a candidate for describing quantum gravity can always do as well as the
LIV-DR by adjusting the model-dependent parameters, but in the same
model-dependent parameters the LIV-DR acts as a more suitable candidate.
