Load balancing routing and quality of transmission (QoT) aware routing have been increasingly studied in mesh wireless networks (WMN) to improve their performance. For the load balancing routing, the traffic bottleneck in the network can be resolved. However, it can decrease QoT because the routes may pass through multiple hops. On the other hand, the QoT aware routing often improves the QoT of the routes, but it can increase the traffic bottleneck due to the unbalanced traffic load in the network. Therefore, the investigation of load balancing routing taking into account QoT is very essential, especially in the case of a wide and ultra-high speed WMN. In this paper, we propose a load balancing routing algorithm under the constraints of QoT for WMN. Our method uses the principle of the software defined networking (SDN) to choose the load balancing routes satisfying the constraints of QoT. Our performance evaluations using OMNeT++ have shown the effectiveness of the proposed algorithm in improving QoT of the data transmission routes, increasing the packet delivery ratio and the network throughput, decreasing the end-to-end delay.