Directional Antennas (DAs) provide higher gain, and reduce interference by directing beams toward the desired receiver. In this paper, we propose a new joint optimization framework considering the energy consumption and throughput in DAs Wireless Mesh Networks (WMNs). We formulate the joint optimization problem as a Mixed Integer Linear Problem (MILP) using a weighted objective function of both the consumed energy and the throughput. We use ILOG Cplex [1], a software based on branch and cut method, to find the optimal solution of the optimization problem. Results prove the efficiency of using DAs in WMNs in the considered scenarios and show that the consumed energy increases with the beamwidth and decreases with the number of power levels when using power control.