In today’s digital era, many applications generate massive data streams that must be sequenced and processed immediately. Therefore, storing large amounts of data for analysis is impractical. Now, this infinite amount of evolving data confronts concept drifts in data stream classification. Concept drift is a phenomenon in which the distribution of input data or the relationship between input data and target label changes over time. If the drifts are not addressed, the learning model’s performance suffers. Non-stationary data streams must be processed as they arrive, and neural networks’ built-in capabilities aid in the processing of huge non-stationary data streams. We proposed an adaptive windowing approach based on a gated recurrent unit, a variant of the recurrent neural network incrementally trained on incoming data (for the real-world airline and synthetic Streaming Ensemble Algorithm (SEA) datasets), and employed elastic weight consolidation with the Fisher information matrix to prevent forgetting. Unlike the traditional fixed window methodology, the proposed model dynamically increases the window size if the prediction is correct and reduces it if drifts occur. As a result, an adaptive recurrent neural network model can adapt to changes in the non-stationary data stream and provide consistent performance. Moreover, the findings revealed that on the airline and the SEA dataset, the proposed model outperforms state-of-the-art methods by achieving 67.74% and 91.70% accuracy, respectively. Further, the results demonstrated that the proposed model has a better accuracy of 3.6% and 1.6% for the SEA and the airline dataset, respectively.