In this chapter, we investigate the kinematic control of a single robot arm with an eye-in-hand camera for visual servoing by using neural networks. The visual servoing problem is formulated as a constrained quadratic program, which is then solved via a recurrent neural network. By this approach, the visual servoing with respect to a static point object is achieved with the feature coordinate errors in the image space converging to zero. Besides, joint angle and velocity limits of the robot arm are satisfied, which thus enhances the safety of the robot arm during the visual servoing process. The performance of the approach is guaranteed via theoretical analysis and validated via a simulative example.