Grasping-force optimization of multifingered robotic hands can be formulated as a problem for minimizing an objective function subject to form-closure constraints and balance constraints of external force. This paper presents a novel recurrent neural network for real-time dextrous hand-grasping force optimization. The proposed neural network is shown to be globally convergent to the optimal grasping force. Compared with existing approaches to grasping-force optimization, the proposed neural-network approach has the advantages that the complexity for implementation is reduced, and the solution accuracy is increased, by avoiding the linearization of quadratic friction constraints. Simulation results show that the proposed neural network can achieve optimal grasping force in real time.