The generalized uncertainty relation is considered in the new equation of state density. Using the WKB approximation, Dirac field entropy of the horizon of the black hole with an internal global monopole is calculated directly. The result shows that the black hole entropy is proportional to the horizon area, which brings to light the relationship between the black hole entropy and the entropy of quantum state near the event horizon. The difference from the brick-wall model is that the present result is convergent without any cutoff. It is indicated that this method can be used to calculate the entropy of the scale field of black hole, and it can be extended to calculate the entropy of Dirac field.