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This paper proposes a QoS active queue management (AQM) mechanism for multi-QoS classes, named as M-GREEN (Global Random Early Estimation for Nipping), which includes the consideration of QoS parameters and provides service differentiation among different flows/classes. M-GREEN extends the concept of ''Random'' and ''Early Detection'' in RED to ''Global Random'' and ''Early Estimation,'' respectively. Furthermore, M-GREEN extends the ''linear'' concept of RED to an ''exponential'' one to enhance the efficiency of AQM. For performance evaluation, extensive numerical cases are employed to compare M-GREEN with some popular AQM schemes and to show the superior performance and characteristics of M-GREEN. Consequently, M-GREEN is a possible way to provide the future multimedia Internet with differential services for different traffic classes of diverse QoS requirements.