This paper gives a theoretical approach to modeling and simulating the Grade of Service (GoS) of Voice over Peerto- Peer Session Initiation Protocol system which is created based on various teletraffic parameters. VoP2P features a particular service characteristic due to its different GoS models originated from circuit switched telephone networks. Especially, most voice session in VoP2P is indirectly connected because peer-nodes usually locate behind NATs. This situation forces peer-node to select one or more relay-node for establishing sessions. However, the relay-node is a constrained resource because every relay-node can only support very limited relay services in VoP2P network. There are two strategies, the S2RS (Staged Single-Relay Strategy) and MRS (Multi-Relay Strategy), to solve the relay-node issue. We adopt three new parameters in VoP2P call-loss models, the first is callee-attendance rate, which is due to the characteristic of destination peer-nodes with a lower attendance probability; the second is call-blocking rate, which is a traditional definition just because the relay-node reaches the limitation of resource; the third is handoff-dropping rate (aka handoff-loss rate), which is caused by the relay-node being removed frequently. The simulation results provide useful reference in the study of teletraffic of VoP2P system.