In this paper, we propose a linear programming model for joint multi-hop routing and scheduling problem in a wireless mesh backhaul network. The network combines wireless mesh backhaul and traditional cellular network, using multiple wireless links for base stations to access wired network through access point. The objective of our model is to determine optimum routing and time-slot allocation of flows in order to maximize the cell throughput that can be provided by wireless BS. It also considers the effect of interference and variable-rate transmission, and uses the typical urban non line-of-sight (NLOS) path loss model. Compared to the single hop cellular network, simulation results under the propagation condition and channel model assumptions show that this scheme achieves significant mesh throughput improvements and range extension. At the same time, by using of the narrow-beam antennas, it can further improve the performance of the network scenarios.