The paper has developed an adaptive control using neural network for controlling a dual-arm robotic system in moving a rectangle object to the desired trajectories. Firstly, the overall dynamics of the manipulators and the object have been derived based on Euler-Lagrangian principle. And then based on the dynamics, a controller has been proposed to achieve the desired trajectories of the grasping object. A radial basis function neural network has been applied to compensate uncertainties of dynamic parameters. The adaptive algorithm has been derived owning to the Lyapunov stability principle to guarantee asymptotical convergence of the closed dynamic system. Finally, simulation work on MatLab has been carried out to reconfirm the accuracy and the effectiveness of the proposed controller.