When LANs are interconnected via an ATM backbone, traffic mismatch between the source LANs and the destination LAN can cause congestion at the destination Interworking Unit (DIWU). In this paper, we present an end-to-end credit-based feedback congestion control scheme that operates on the LAN side of the LAN/ATM interface. The scheme ensures that there is no packet loss at DIWU due to buffer overflow. It provides fair allocation to the source traffic demand in a max-min fashion and achieves maximum throughput possible at all level of loading conditions. The results of simulation conducted on various traffic patterns clearly demonstrate that the optimal buffer sizing at DIWU achieves minimum delay and maximum throughput at the same time.