The stability and security management of IT data becomes more important because information security threats increases rapidly in Big Data era. The operational policy of the data backup considering information security threats is required because the backup policy is the fundamental method that prevents the damage of security threats. We present an economic approach for a data backup system with information security threats which damage the system. The backup operation consists of the differential backup and the batch backup. We present a stochastic model considering the occurrence of information security threats and their damage. We analyze the stochastic model to derive the performance measures for the cost analysis. Finally we analyze the average cost of the system and give numerical examples.