This paper presents an efficient routing algorithm for the Mesh-Hypercube (M-H) network. The M-H network is one of the new interconnection networking techniques use to build high performance parallel computers. The combination of M-H networks offers high connectivity among multiple nodes, fault-tolerance, and load scalability. However, the performance of M-H networks may degrade significantly in the presence of frequent link or node failures. When a link or node failure occurs, neither the hardware schemes nor point to point and multistage routing algorithms can be used without adding extra links. This paper presents an efficient single bit store and forward (SBSF) routing algorithm for M-H network that based on the round robin scheduling algorithm. Simulation and numerical results suggest that the proposed routing algorithm improves the overall performance of M-H network by both reducing the transmission delay and increasing the total data throughput even in the presence of faulty nodes.