Asynchronous Transfer Mode was designed for multimedia communication networks. In multimedia networks, there are various kinds of data with different Quality of Service (QoS) requiring transmitting. Consequently, the control of QoS in ATM becomes very important. Therefore, this paper proposes a novel buffer management algorithm named GREEN (Global Random Early Estimation for Nipping cells). In buffer management, to drop a cell randomly and early is the main stream. Specifically, the designed random probability function considers not only network statuses but also QoS requirements. Also, GREEN speeds up the decision making by Early Estimation. The properties of "Global Random" and "Early Estimation" of the GREEN algorithm are obtained by globally considering the delay requirement and early estimating the queue length for decision making.