As the technology scales toward deeper submicron, system-on-chip designs have migrated from fairly simple single processor and memory designs to relatively complicated systems with higher communication requirements. Network-on-chip architectures emerged as promising solutions for future system-on-chip communication architecture designs. However, the switching and routing algorithm design of network-on-chip communication architectures are still facing great challenges. To address the deficiencies of the existing routing algorithms, a new deterministic network-on-chip routing algorithm: ZigZag routing algorithm is proposed in this paper. The specifics of the algorithm as well as the simulation results and analysis are also presented. For the proposed ZigZag algorithm, the X direction and Y direction distances are compared. The packets are sent in the direction with the greater distance until they become equal at which point, the packets sent alternates between the X direction and the Y direction until they reach their destination. Simulation of the proposed ZigZag routing algorithm and two existing routing algorithms have been carried out on NIRGAM network-on-chip simulator. Simulation results illustrate that the performance of the ZigZag routing algorithm matches or exceeds the performance of the existing routing algorithms.