Unbalance between user requirements and insufficient network resources makes a congestion. In the future since the communication networks will have very heavy traffic congestion will be more serious. The ATM networks was recommended to support the B-ISDN service for the future multimedia communication. In thie sense of congestion avoidance and recovery the ABR service category in ATM networks allows the feedback flow control mechanism to dynamically allocate the idle bandwidth of the network to users fairly and to control the network congestion rapidly In this paper we introduce a congestion control scheme using systematical approach to confirm robust stability with respect to unknown round trip delay for the network which has both unicast and multicast connections.