WiMAX mesh mode, recently standardized, enables direct communications between subscriber stations without referring to the base station (BS). It can be a great solution for providing access in hard-to-wire areas and especially in extending the coverage of the BS. In this paper, we propose a joint routing and scheduling algorithm for improving the performance of WiMAX mesh networks in terms of throughput. Our routing algorithm selects highest end-to-end data rate paths for maximizing the network capacity. The scheduling algorithm ensures best scheduling on the selected links for maximizing network utilization, and guarantees fairness as well. We show by numerical simulations that the proposed joint routing and scheduling algorithm, significantly increases the network capacity and utilization while ensuring fairness.