Hierarchical identity-based signature (HIBS) has wide applications in the large network. However,the existing works cannot solve the trade-off between the security and efficiency. The main challenge at present is to construct a high efficient and strong secure HIBS with a low computation cost. In this paper,a new construction of HIBS scheme is proposed. The new scheme achieves the adaptive security which is a strong security in the identity-based cryptography. But our scheme has short public parameters and the private keys size shrinks as the hierarchy depth increases. The signature size is a constant and the cost of verification only requires four bilinear pairings,which are independent of hierarchy depth. Furthermore,under the q-strong computational diffie-Hellman problem (q-SDH) assumption,the scheme is provably secure against existential forgery for adaptive chosen message and identity attack in the standard model. Hierarchical identity-based signature (HIBS) has wide applications in the large network. However, the existing works can not solve the trade-off between the security and efficiency. The main challenge at present is to construct a high efficient and strong secure HIBS with a low computation cost. In this paper, a new construction of HIBS scheme is proposed. The new scheme achieves the adaptive security which is a strong security in the identity-based cryptography. But our scheme has short public parameters and the private keys size shrinks as the hierarchy size increases increases. The signature size is a constant and the cost of verification requires only four bilinear pairings, which are independent of hierarchy depth. Furthermore, under the q-strong computational diffie-Hellman problem (q-SDH) assumption, the scheme is provably secure against existential forgery for adaptive chosen message and identity attack in the standard model.