In the field of redundant manipulator control, accurate position/orientation control (POC) is the key to completing complex tasks. However, traditional robot control methods based on quadratic programming (QP) often ignore the accurate control of orientation, which limits the ability of robots to perform complex and high-precision tasks. To this end, this paper deeply analyzes the rotation matrix, derives the equality constraints of the end-effector orientation control, and proposes a QP-based redundant manipulator control scheme, which integrates the equality constraints of the end-effector position/orientation into the QP framework. Simultaneously, a dynamic neural network (DNN) is devised to address the POC issue. The stability of the DNN is analyzed by the Lyapunov method, and the global convergence of the DNN is proved. Simulations demonstrate the controller’s excellent POC and tracking accuracy.