Since the evolution of the internet, many small and large companies have moved their business to the internet to provide services to customers worldwide. To understand how cyber credit card fraud are being committed, in this we study the different types of cyber fraudsters that commit cyber credit card fraud and the techniques used by these cyber fraudsters to commit fraud on the internet is discussed. Fraud detection is a technique of identifying prohibited acts that are occurring around the world. Therefore, the need to ensure secure transactions for credit-card owners. This system implements the supervised anomaly detection algorithm of Data mining to detect fraud in a real time transaction on the internet, and thereby classifying the transaction as legitimate, suspicious fraud and illegitimate transaction. The anomaly detection algorithm is designed on the Neural Networks which implements the working principal of the human brain. The techniques of Data mining are also popular in detecting cyber credit-card fraud. An effective use of data mining techniques and its algorithms can be implemented to detect or predict fraud through Knowledge Discovery from unusual patterns from gathered data set. In this paper, we discussed about the various credit-card fraudsters techniques and also the detection methods for cyber credit card transactions. The goal of this paper is to provide a system’s model for cyber credit card fraud detection and a comprehensive review of Hidden Markov Model (HMM) and Neural Networks (NN) techniques to detect credit card fraudulent in an effective way.