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In this paper, by using quantum statistical methods, we directly obtain the partition function of Bose field and Fermi field on the background of the axisymmetrical Sen black hole. The difficult-to-solve wave equation is avoided. Then via the improved brick-wall method and membrane model, we calculate the entropy of Bose field and Fermi field of the black hole. We find that the entropy of the black hole is proportional to the area of the horizon. In our results, we do not encounter the left out term nor the divergent logarithmic term that appears in the original brick-wall method. The question that arose in the brick-wall method of whether the entropy of the scalar or Dirac fields outside the event horizon is the entropy of the black hole does not arise in the present method. The influence of spinning degeneracy of particles on entropy of the black hole is also given. We provide a way to study various complicated black holes. [ABSTRACT FROM AUTHOR]