This paper proposes a novel call admission control scheme capable of providing a combination of call and packet level quality of service requirements in cellular packet networks. Specifically, we propose a distributed call admission control scheme called PFG, which maximizes the wireless channel utilization subject to a predetermined bound on the call dropping and packet loss probabilities for variable-bit-rate traffic in a packet-switched wireless cellular network. We show that in wireless packet networks, the undesired event of dropping an ongoing call can be completely eliminated without sacrificing the bandwidth utilization. Extensive simulation results confirm that our scheme satisfies the hard constraint on call dropping and packet loss probabilities while maintaining a high bandwidth utilization.