Recently, Au et al. proposed a practical hierarchical identity-based encryption (HIBE) scheme and a hierarchical identity-based signature (HIBS) scheme. In this paper, we point out that there exists security weakness both for their HIBE and HIBS scheme. Furthermore, based on q-ABDHE, we present a new HIBE scheme which is proved secure in the standard model and it is also efficient. Compared with all previous HIBE schemes, ciphertext size as well as decryption cost are independent of the hierarchy depth. Ciphertexts in our HIBE scheme are always just four group elements and decryption requires only two bilinear map computations.