A closed analytical model is developed for the performance analysis of wireless multi-hop path. The research first analyzed the interference within the multi-hop path which is the cause of the intra-flow contention problem and derived the model for its quantitative calculation, and then it modeled the multi-hop path as a queuing network and derived its analytical model for performance analysis based on diffusion approximation method. Finally it calculated the capacity of the multi-hop path under the constraint of network stability. This model can be used to explore the transmission capacity of the multi-hop wireless networks and to analyze its ability to support QoS applications. The accuracy of the proposed model is validated through comparing the numerical results and the simulation results.