The privacy model of radio frequency identification (RFID) systems is for formalizing the adversarial capabilities and the security requirements of RFID anonymity and untraceability. Existing unpredictability-based privacy models such as unp-privacy, eunp-privacy, unp*-privacy, and unpτ-privacy have captured different kinds of practical attacks, and some of them also have mutual authentication included. However, forward privacy, which allows a tag to remain untraceable even after its corruption, is yet to be well captured in any unpredictability-based privacy models. In this paper, we describe some forward privacy-related attacks that can be launched against RFID tags in practice. We then propose a new unpredictability-based forward privacy model called unpfτ-privacy. It extends an existing one called unpτ-privacy, which has been shown to be stronger than ind-privacy, unp-privacy, and unp*-privacy. We also propose an RFID protocol that supports forward privacy and mutual authentication. We show that it can be proven secure in the unpfτ-privacy mode