In this paper, we propose the new rate-based transmission rates control algorithm that allocates the fair band-width for ABR service in ATM network. In the traditional ABR service, bandwidth is allocated with constant rate increment or decrement, but in the proposed algorithm, it is allocated fairly to the connected calls by the fuzzy inference of the available bandwidth. The fuzzy inference uses buffer state and the buffer variant rate as the input variables, and uses the total transmission rate as a output variable. This inference a bandwidth is fairly distributed over all ABR calls in service. By simmulation, we showed that the proposed method improved 0.17% in link effectiveness when RIF, RDF is 1/4, 38.6% when RIF, RDF 1/16, and 82.4% when RIF, RDF 1/32 than that of the traditional EFPCA.