Hu, Huang and Fan proposed a fully secure hierarchical identity-based encryption (IEICE Trans. Fundamentals, Vol.E92-A, No.6, pp.1494–1499, 2009) that achieves constant size of ciphertext and tight security reduction. Unfortunately, Park and Lee (IEICE Trans. Fundamentals, Vol.E93-A, No.6, pp.1269–1272, 2010) found that the security proof of Hu et al.'s scheme is incorrect; that is, the security of Hu et al.'s scheme cannot be reduced to their claimed q-ABDHE assumption. However, it is unclear whether Hu et al.'s scheme is still secure. In this letter, we provide an attack to show that the scheme is not secure against the chosen-plaintext attack.