As Chronic Kidney Disease progresses slowly, early detection and effective treatment are the only cure to reduce the mortality rate. Machine learning techniques are gaining significance in medical diagnosis because of their classification ability with high accuracy rates. The accuracy of classification algorithms depend on the use of correct feature selection algorithms to reduce the dimension of datasets. In this study, Support Vector Machine classification algorithm was used to diagnose Chronic Kidney Disease. To diagnose the Chronic Kidney Disease, two essential types of feature selection methods namely, wrapper and filter approaches were chosen to reduce the dimension of Chronic Kidney Disease dataset. In wrapper approach, classifier subset evaluator with greedy stepwise search engine and wrapper subset evaluator with the Best First search engine were used. In filter approach, correlation feature selection subset evaluator with greedy stepwise search engine and filtered subset evaluator with the Best First search engine were used. The results showed that the Support Vector Machine classifier by using filtered subset evaluator with the Best First search engine feature selection method has higher accuracy rate (98.5%) in the diagnosis of Chronic Kidney Disease compared to other selected methods.