RFID privacy problems will have to be solved before items with RFID tags can be safely provided to consumers on a large scale. Here, we considered the location privacy problem of unauthorized persons or agents being able to trail a person by tracing a unique ID recorded in an attached RFID tag. We proposed a method for using RFID tags that include an interrogator with an algorithm to generate RFID passwords. This method groups RFID passwords for RFID tags in a way that protects consumer privacy. We simulated the possibility of trailing a consumer in a shopping mall. We investigated how much the traceability of a consumer changed when the proposed method was applied. Simulation results showed that the traceability fell by about 0.4% when the influence level of RFID password leakage was 2% in this model. In practice, it may be difficult to read a consumer's RFID tag from distances like those assumed in this simulation because RFID is easily influenced by various environmental conditions. However, even if invasion of privacy is technically difficult, consumers will remain concerned as long as there is any possibility of invasion of privacy through RFID. Therefore, our proposed method will be useful for RFID system application.