Many people expect robots to assist us in our daily lives. In this case, visual information is necessary in human-robot cooperation. In general, by using visual information feedback, the posture error between manipulators and fingers is computed to adjust the system input. Because robotic manipulators have redundant degree-of-freedom (DOF), a variety of tasks can be performed at the same time. However, conflicts may occur between tasks and the stability of the system cannot be guaranteed. The control spaces of redundant manipulators are divided into work-space and null-space. As the number of the DOF increases, the calculation of the null-space term becomes more complicated. This paper describes a novel approach of advanced observer design of visual feedback redundant manipulators by using the task-priority control strategy. In order to avoid the conflicts of multiple tasks, the task-priority control strategy is employed in our system. In the proposed approach, a RIC structure based work-space observer is designed. We also utilize this work-space observer in hierarchical null-spaces to simplify the calculation. The validity of the proposed approach is verified by a simulation. The results suggest that the proposed work-space observer has better performance than the conventional work-space observer in hierarchical null-spaces.