Applying the new equation of state density motivated by the generalized uncertainty relation in the quantum gravity field，we investigate the black hole entropy on the background of three-dimensionnal BTZ. When the λ with the Planck scale，and relative to the dimensions of spacetime introduced in generalized uncertainty relation has a fixed value，we obtain the Bekenstein-Hawking entropy of BTZ black hole and the correction term. Because we have used the new equation of state density，in our results the divergence term appearing in the brick-wall model is removed，at the same time with holding the small mass approximation. Thus the correction value of the Bekenstein-Hawking entropy of the black hole is derived from the quantum statistical view. It depends the understanding of the correction value of the black hole entropy.