Chronic kidney disease (CKD) is a progressive loss in kidney function. Early detection of patients who will progress to late-stage CKD is of paramount importance for patient care. To address this, we develop a pipeline to process longitudinal electronic heath records (EHRs) and construct recurrent neural network (RNN) models to predict CKD progression from stages II/III to stages IV/V. The RNN model generates predictions based on time-series records of patients, including repeated lab tests and other clinical variables. Our investigation reveals that using a single variable, the recorded estimated glomerular filtration rate (eGFR) over time, the RNN model achieves an average area under the receiver operating characteristic curve (AUROC) of 0.957 for predicting future CKD progression. When additional clinical variables, such as demographics, vital information, lab test results, and health behaviors, are incorporated, the average AUROC increases to 0.967. In both scenarios, the standard deviation of the AUROC across cross-validation trials is less than 0.01, indicating a stable and high prediction accuracy. Our analysis results demonstrate the proposed RNN model outperforms existing standard approaches, including static and dynamic Cox proportional hazards models, random forest, and LightGBM. The utilization of the RNN model and the time-series data of previous eGFR measurements underscores its potential as a straightforward and effective tool for assessing the clinical risk of CKD patients concerning their disease progression.