In this paper, I propose Fuzzy Policing Mechanism(FPM) over ATM networks for the control of traffic which is unpredictable and bursty source. The FPM is consist of counter, subtracter and Fuzzy Logic Controller(FLC). The FLC is divided to fuzzifier, inference engine and defuzzifer The output of FLC inputs to the subtractor and it controls the counter. The counter works as a switch in transmission of cells. In simulation, I compared the FPM with the Leaky Bucket algorithm(LBM) in cell loss probability and performance characteristics. As a result, FPM gives lower cell loss probability than that of LBM and has good response behavior The FPM efficiently controls the transmission of packets which are variable traffic source and, it also has good selectivity.