Feature selection is the first and most essential process for developing predictive models using complex medical datasets such as that of Chronic Kidney Disease (CKD). This paper proposes a new hybrid feature selection model, which integrates Simulated Annealing (SA) and Recursive Feature Elimination (RFE), for improving CKD diagnosis by Feed forward Neural Networks (FNN). The SA algorithm provides a global search mechanism, which is used to get potential feature subsets. RFE then iteratively improves these subsets by eliminating the least significant features on basis of model performance. Hybrid methodology provides an accurate and effective feature selection procedure by combining the benefits of both. The approach is validated using the CKD dataset provided by the UCI Repository. Evaluation criteria portrays that the proposed strategy achieves 94% accuracy, 0.93 precision, 0.91 recall, and an F1-score of 0.94which is much better than other hybrid feature selection techniques. The results obviously indicate that the SA-RFE hybrid approach significantly enhance the detection performance for CKD using FNN, which could be a potential assistant tool in diagnosis with improved accuracy.