This paper presents the performance modeling, analysis, and simulation of SIP-T (Session Initiation Protocol for Telephones) signaling system in carrier class VoIP (Voice over IP) network. The SIP-T signaling system defined in IETF (Internet Engineering Task Force) draft is a mechanism that uses SIP (Session Initiation Protocol) to facilitate the interconnection of PSTN with carrier class VoIP network. Based on IETF, the SIP-T signaling system not only promises scalability, flexibility, and interoperability with PSTN but also provides call control function of MGC (Media Gateway Controller) to set up, tear down, and manage VoIP calls in carrier class VoIP network. In this paper, we analyze the queueing size (i.e. buffer size), the mean of queueing delay, and the variance of queueing delay of SIP-T signaling system that are the major performance evaluation parameters for improving QoS (Quality of Service) and system performance of MGC in carrier class VoIP network focused on toll by-pass or tandem by-pass of PSTN. First, we assume a mathematical model of the M/G/1 queue with non-preemptive priority assignment to represent SIP-T signaling system. Second, we present the formulas of queueing size, queueing delay, and delay variation for the non-preemptive priority queue by queueing theory respectively. Besides, some numerical examples of queueing size, queueing delay, and delay variation are presented as well. Finally, the theoretical estimates are shown to be in excellent consistence with simulation results.