The configuration of the optimization results based on the directional manipulability is not the best flexible configuration if considering the energy consumption. A new dexterity indexes—energy constraint directional manipulability was proposed to evaluate the dexterity of manipulator on the task direction based on the same energy constraint criteria. The simulation demonstrates that the dexterity of the configuration is the best on the task direction that optimized by the energy constraint directional manipulability as the objective function when considering the energy consumption. In the joint trajectory planning, this dexterity indexes can be used as the performance index to improve the operation configuration of the robot, and improve the dexterity of the robot on the task direction.