In this paper we develop an analytical threshold-based bandwidth allocation policy for 3G multi-class cellular networks. We consider the effects of user mobility when the cellular network supports multiple classes of connections having different QoS bandwidth requirements. The policy gives priority to handoff connections over new calls and prioritizes between different classes of handoff connections according to their QoS constraints by assigning a maximum occupancy, i.e. a threshold, to each connection class. The policy can be modeled as a multi-dimension Markov chain, and therefore, a product form solution is provided. The QoS metrics - new call blocking probability, handoff call dropping probability, and probability of unsuccessful call completion - are derived. We show numerically that this policy improves the service quality by minimizing handoff dropping probability and maximizing the bandwidth utilization i.e. by minimizing the new call blocking probability.