In our previous work, a Multi-Path Routing (MPR) scheme was proposed to maximize the data throughput for torus-based NoCs by utilizing multiple paths for concurrent data transmission. In this paper, a deadlock-free virtual channel model is proposed for the MPR scheme. In this virtual channel model, every physical channel on the network is split into about 3.5 virtual channels on average. It is proved that any minimal routing algorithm (including the MPR scheme) using this model is deadlock-free. The MPR scheme employing this new virtual channel model is still a fully adaptive one. The performance of the MPR scheme using the proposed virtual channel model is evaluated through simulations and compared with the fully adaptive Single-Path minimal Routing (SPR) scheme with the same virtual channel model. Simulation results show that MPR achieves better average message latency and normalized accepted traffic than SPR under both uniform and nonuniform traffic in general.