A novel neural network (NN)-based optimal adaptive consensus control scheme is introduced in this paper for networked mobile robots in the presence of unknown robot dynamics. Throughout the paper, two NNs are used. The unknown formation dynamics of each robot is identified by using the first NN. The second NN is utilized to approximate a novel value function derived in this paper as a function of augmented error vector, which is comprised of the regulation and consensus-based formation errors of each robot. A novel near optimal controller is developed by using approximated value function and identified formation dynamics. The Lyapunov stability theorem is employed to derive the NN weight tuning laws and demonstrate the consensus achievement of the overall formation. The simulation results are depicted to show performance of our theoretical claims.