A statistical call admission control (CAC) allows more calls with on-off patterns to be accepted and a higher channel efficiency to be achieved. In this paper, we propose three statistical CACs for VoIP calls with silence suppression considering the priority of each VoIP call, where the call priority is determined by the call acceptance order in an IP-PBX. We analyse the packet loss rates in an IP-PBX under the proposed strategies and express the end-to-end QoS of a VoIP call as an R-factor in a VoIP service network. The performances of the proposed CACs are evaluated using the maximum allowable number of VoIP calls while satisfying the end-to-end QoS constraint, the average QoS of acceptable VoIP calls and the channel efficiency. The advantage of the proposed statistical CACs over the non-statistical CAC is verified in terms of these three performance metrics. The results indicate that a trade-off is possible in that the maximum allowable number of VoIP calls in an IP-PBX increases as the average QoS of acceptable VoIP calls is lowered according to the proposed statistical CAC used. Nevertheless, the results allow us to verify that the channel efficiencies are the same for all the statistical CACs considered.