Centralized routing is beneficial as it provides a global network view to plan and achieve the best and effective path for real-time traffic. With the rapid development of software defined networking, centralized routing has aroused more and more concern of researchers. An effective centralized load balancing routing (LBR) for wireless mesh network considering energy harvesting is proposed in this letter. LBR can provide flexible and optimal routes for real-time traffic. To minimize the long-term weighted sum cost which includes load and energy condition, LBR considers the queue length, channel condition, energy cost and energy harvesting. The problem of making dynamic decisions based on real-time traffic conditions is solved by the dynamic programming approach. Simulation results demonstrate the advantages of LBR.