Identity based signcryption (IBSC) is a novel cryptographic primitive that simultaneously provides the authentication and encryption in a single logic step. The IBSC has been shown to be useful in many applications, such as electronic commerce, mobile communications and smart cards. Recently, Li et al. (2013) [16] proposed a new identity based signcryption scheme and claimed that their scheme was provably secure in the standard model, i.e. (IND-IBSC-CCA2) semantically secure under adaptively chosen-ciphertext attack and (EUF-IBSC- CMA) existential unforgeable under adaptively chosen- message. However, in this paper, by giving concrete at- tacks, we show that Li et al's scheme is not secure in their security model. Additionally, we further indicate that Li et al's scheme also does not satisfy strongly existential unforgeability.