This paper proposes a primal-dual neural network with a one-layer structure for online resolution of constrained kinematic redundancy in robot motion control. Unlike the Lagrangian network, the proposed neural network can handle physical constraints, such as joint limits and joint velocity limits. Compared with the existing primal-dual neural network, the proposed neural network has a low complexity for implementation. Compared with the existing dual neural network, the proposed neural network has no computation of matrix inversion. More importantly, the proposed neural network is theoretically proved to have not only a finite time convergence, but also an exponential convergence rate without any additional assumption. Simulation results show that the proposed neural network has a faster convergence rate than the dual neural network in effectively tracking for the motion control of kinematically redundant manipulators.