Hydrogen plays a crucial role in improving sustainability and offering a clean and efficient energy carrier that significantly reduces greenhouse gas emissions. However, the primary method of industrial hydrogen production, steam methane reforming (SMR), relies on the combustion of hydrocarbons as the heating source for the reforming reactions, resulting in significant carbon emissions. To address this issue, an experimental setup of an electrically-heated steam methane reformer (e-SMR) has been constructed at UCLA, and a lumped first-principle dynamic process model was built based on parameters estimated from the experimental data in a previous study. Subsequently, the first-principle dynamic process model was implemented into the computational model predictive control (MPC) scheme, successfully driving the hydrogen production rate to the desired setpoint. While these works are important and pave the way for developing MPC for large-scale e-SMR processes, the first-principle process model may not accurately reflect the actual process behavior, particularly as the process behavior changes with time. Therefore, the development and establishment of an adaptive data-driven approach for implementing model predictive control in the e-SMR process is necessary. To address this need, the present work investigates the construction of recurrent neural network (RNN) models for an e-SMR process in-depth, utilizing data from an experimentally-validated first-principle model. Specifically, a long short-term memory (LSTM) layer was utilized in the RNN model to effectively capture the complex correlations present in long-term sequential data. Subsequently, this LSTM-based RNN process model was employed to design an MPC, and its performance was evaluated through comparison with proportional–integral (PI) control. To address potential disturbances and variability in a typical e-SMR process, three distinct approaches were developed: MPC with an integrator, MPC with real-time online retraining (transfer learning), and offset-free MPC. These approaches effectively eliminated the offset caused by disturbances. Overall, this study underscores the effectiveness of utilizing RNN models to capture process dynamics in an experimental e-SMR process. It also outlines strategies for employing RNN-based control and multiple approaches to address disturbances in general processes with partially infrequent and delayed measurement feedback. This approach is particularly valuable in scenarios where developing first-principle models for a new process may be challenging.