We propose burst based bandwidth reservation method called FRP (Fast Reservation Protocol) in ATM LAN with general topology, and evaluate its performance. In FRP, the bandwidth is allocated on each link on burst basis, not on call basis. This enables an effective use of network resources when it is applied to highly bursty traffic, which can be typically found in data communications. The problem of FRP is that VCs traversing the different number of links experience different blocking probabilities as can be found in the conventional circuit-switching networks. In this paper, we treat a fairness issue in FRP-based ATM local area networks. The Max-Min flow control is adopted as the fair bandwidth allocation method to accomplish the fairness in the throughput. However, the original Max-Min flow control works in a centralized fashion, which is not desirable in the FRP-based ATM LAN. We therefore propose a "semi"-distributed Max-Min flow control suitable to FRP, in which each switch maintains its own local information about bandwidth usage of the connected links. Through simulation experiments, we show that the proposed semi-distributed Max-Min flow control can achieve the fairness among VCs as the original Max-Min flow control when the propagation delays are not large and the number of VCs is not so much.