The last few years witnessed a great and increasing interest in the field of intelligent classification techniques which rely on Machine Learning. In recent times Machine Learning one of the areas in Artificial Intelligence has been widely used in order to assist medical experts and doctors in the prediction and diagnosis of different diseases. In this paper, we applied two different machine learning algorithms to a problem in the domain of medical diagnosis and analyzed their efficiency in prediction the results. The problem selected for the study is the diagnosis and factors affecting Chronic Kidney Disease. The dataset used for the study consists of 153 cases and 11 attributes of CKD patients. The objective of this research is to compare the performance of Artificial Neural Networks (ANNs) and Logistic Regression (LR) classifier on the basis of the following criteria: Accuracy, Sensitivity, Specificity, Prevalence, and Area under curve (ROC) for CKD prediction. From the experimental results, it is observed that the performance of ANNs classifier is better than the Logistic Regression model. With the accuracy of 84.44%, sensitivity of 84.21%, specificity of 84.61% and AUCROC of 84.41%. Also, through the final fitted models used, the most important factors that have a clear impact on chronic kidney disease patients are creatinine and urea.