Customer behavior prediction is gaining more importance in the banking sector like in any other sector recently. This study aims to propose a model to predict whether credit card users will pay their debts or not. Using the proposed model, potential unpaid risks can be predicted and necessary actions can be taken in time. For the prediction of customers' payment status of next months, we use Artificial Neural Network (ANN), Support Vector Machine (SVM), Classification and Regression Tree (CART) and C4.5, which are widely used artificial intelligence and decision tree algorithms. Our dataset includes 10713 customer's records obtained from a well-known bank in Taiwan. These records consist of customer information such as the amount of credit, gender, education level, marital status, age, past payment records, invoice amount and amount of credit card payments. We apply cross validation and hold-out methods to divide our dataset into two parts as training and test sets. Then we evaluate the algorithms with the proposed performance metrics. We also optimize the parameters of the algorithms to improve the performance of prediction. The results show that the model built with the CART algorithm, one of the decision tree algorithm, provides high accuracy (about 86%) to predict the customers' payment status for next month. When the algorithm parameters are optimized, classification accuracy and performance are increased.