In this paper, an extended linearized neural state space (ELNSS) topology is proposed, where an ELNSS based modeling and control strategy for a class of nonlinear systems is presented. In terms of the modeling, the extended Kalman filter (EKF) algorithm is used to train the parameters inside the ELNSS model, where a high order correlation method is applied to validate the estimated model. This is then followed by the design of a one-step-ahead predictive controller for affine nonlinear systems. The stability of the so-formed closed loop control system is investigated, and several sufficient conditions that guarantee the local asymptotic stability are established. Two simulation examples are used to demonstrate the proposed algorithm and desired results have been obtained.