Kidney diseases can cause severe morbidity, mortality, and health burden. Determining the risk factors associated with kidney damage and deterioration has become a priority for the prevention and treatment of kidney disease. This study followed 497 patients with stage 3–5 chronic kidney disease (CKD) who were treated at the ward of Taipei Veterans General Hospital from January 2006 to 2019 in Taiwan. The patients underwent 3-year-long follow-up sessions for clinical measurements, which occurred every 3 months. Three time-dependent survival models, namely the Cox proportional hazard model (Cox PHM), random survival forest (RSF), and an artificial neural network (ANN), were used to process patient demographics and laboratory data for predicting progression to renal failure, and important features for optimal prediction were evaluated. The individual prediction of CKD progression was validated using the Kaplan–Meier estimation method, based on patients’ true outcomes during and beyond the study period. The results showed that the average concordance indexes for the cross-validation of the Cox PHM, ANN, and RSF models were 0.71, 0.72, and 0.89, respectively. RSF had the best predictive performances for CKD patients within the 3 years of follow-up sessions, with a sensitivity of 0.79 and specificity of 0.88. Creatinine, age, estimated glomerular filtration rate, and urine protein to creatinine ratio were useful factors for predicting the progression of CKD patients in the RSF model. These results may be helpful for instantaneous risk prediction at each follow-up session for CKD patients.