Abstract: Hierarchical identity based signature (HIBS) has wide application in large scale networks. However, the existing work cannot solve the trade-off between security and efficiency. The main challenge at present is to construct a high efficient and strongly secure HIBS with low computation cost. To overcome the drawbacks in the previous work, a new hierarchical identity-based signature scheme is introduced. The proposed scheme has some advantages over the available. For examples, the private keys size shrinks as the identity depth increases, the signature only consists of three group elements and three bilinear pairs are needed in verifying algorithm, which are independent of hierarchy depth. Furthermore, the security of the new scheme is based on the general selective-identity security model(Gs-ID) which is a general security model based on full security model and selective identity model. Under the h-computational Diffie-Hellman exponent problem (h-CDH) assumption, our scheme is proven to be secure against Gs-ID and adaptive chosen message attack. In addition, the security analysis does not rely on the random oracles. The assumption in our scheme is more natural than many of the hardness assumptions recently introduced to HIBS in the standard model, which solves the trade-off between the security and computation efficiency.