Most of the policing techniques proposed so far in high speed networks using the ATM technique are based on conventional approaches which use a crisp decision making logic. They don't meet the selectivity and responsiveness requirements needed to make a policing efficient. In this paper we propose a policing mechanism based on fuzzy logic. The main characteristics of the proposed fuzzy policer are simplicity and the capacity to combine a high degree of responsiveness with a selectivity close to that of an ideal policer. Moreover, it can easily be implemented in hardware, thus enhancing both cost and processing performance. The simulation results reported show that the performance of our fuzzy policer is much better than that of conventional policing mechanisms