Fuzzy identity based encryption (FIBE), proposed by Sahai and Waters, is a new kind of identity based encryption. It allows users with identity w can decrypt ciphertext for w' if and only if w is close enough to w'. Recently, Ren et al. proposed a new FIBE scheme and claimed it is fully CCA2 secure in the standard model with a tight reduction. However, in this paper we will show that their scheme is not correct. Furthermore, the key generation process of their scheme cannot resist the collusion attack, which is a basic security requirement for FIBE. At last, we propose a new fully secure FIBE scheme based on the Sahai–Waters FIBE scheme and prove its security by using the “dual system encryption” technique.