With the developments in information technology and improvements in communication channels, fraud is spreading all over the world, resulting in huge financial losses. Though fraud prevention mechanisms such as CHIP&PIN are developed, these mechanisms do not prevent the most common fraud types such as fraudulent credit card usages over virtual POS terminals through Internet or mail orders. As a result, fraud detection is the essential tool and probably the best way to stop such fraud types. In this study, classification models based on Artificial Neural Networks (ANN) and Logistic Regression (LR) are developed and applied on credit card fraud detection problem. This study is one of the firsts to compare the performance of ANN and LR methods in credit card fraud detection with a real data set.