We propose an improved offset-free model predictive control (MPC) framework, which learns and utilizes the intrinsic model-plant mismatch map, to effectively exploit the advantages of model-based and data-driven control strategies and overcome the limitation of each approach. In this study, the model-plant mismatch map on steady-state manifold is approximated via artificial neural network (ANN) modeling based on steady-state data from the process. Though the learned model-plant mismatch map can provide the information at the equilibrium point (i.e., setpoint), it cannot provide model-plant mismatch information during transient state. To handle this, we additionally apply a supplementary disturbance variable which is updated from a revised disturbance estimator considering the disturbance value obtained from the learned model-plant mismatch map. Then, the learned and supplementary disturbance variables are applied to the target problem and finite-horizon optimal control problem of the offset-free MPC framework. By this, the control system can utilize both the learned model-plant mismatch information and the stabilizing property of the nominal disturbance estimator. The closed-loop simulation results demonstrate that the proposed offset-free MPC scheme utilizing the model-plant mismatch map learned via ANN modeling efficiently improves the closed-loop reference tracking performance of the control system. Additionally, the zero-offset tracking condition of the developed framework is mathematically examined.