We propose a system for mobile-phone fraud detection based on a bidirectional artificial neural network (bi-ANN). The key advantage of such a system is the ability to detect fraud not only by offline processing of call detail records (CDR), but also in real time. The core of the system is a bi-ANN that predicts the behavior of individual mobile-phone users. We determined that the bi-ANN is capable of predicting complex time series (Call_Duration parameter) that are stored in the CDR.