In this paper, to diminish discontinuity points arising in the infinity-norm velocity minimization scheme, a bi-criteria velocity minimization scheme is presented based on a new neural network solver, i.e., an LVI-based primal-dual neural network. Such a kinematic planning scheme of redundant manipulators can incorporate joint physical limits, such as, joint limits and joint velocity limits simultaneously. Moreover, the presented kinematic planning scheme can be reformulated as a quadratic programming (QP) problem. As a real-time QP solver, the LVI-based primal-dual neural network is developed with a simple piecewise linear structure and high computational efficiency. Computer simulations performed based on a PUMA560 manipulator model are presented to illustrate the validity and advantages of such a bi-criteria velocity minimization neural planning scheme for redundant robot arms.