The security of any system is a key factor toward its acceptability by the general public. We propose an intuitive approach to fraud detection in financial institutions using machine learning by designing a Hybrid Credit Card Fraud Detection (HCCFD) system which uses the technique of anomaly detection by applying genetic algorithm and multivariate normal distribution to identify fraudulent transactions on credit cards. An imbalance dataset of credit card transactions was used to the HCCFD and a target variable which indicates whether a transaction is deceitful or otherwise. Using F-score as performance metrics, the model was tested and it gave a prediction accuracy of 93.5%, as against artificial neural network, decision tree and support vector machine, which scored 84.2%, 80.0% and 68.5% respectively, when trained on the same data set. The results obtained showed a significant improvement as compared with the other widely used algorithms.