Abstract. By using the method of quantum statistics, we directly derive the partition function of bosonic and fermionic field under the back-ground of rotating U(1)×U(2) Dilaton black hole. The difficulty in solving the wave equation is avoided. Then via the improved brick-wall method, membrane model, we calculate the entropy of bosonic and fermionic field. We obtain that the entropy of black hole is proportional to the area of horizon. The stripped term and the divergent logarithmic term in the original brick-wall method no longer exist. Why the entropy of the scalar or Dirac field out side the event horizon is the entropy of black hole is solved. We offer a new simple and direct way of calculating the entropy of various complicated black hole.

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