Hierarchical identity based cryptography is a generalization of identity based encryption that mirrors an organizational hierarchy. It allows a root public key generator to distribute the workload by delegating public key generation and identity authentication to lower-level public key generators. Most hierarchical identity based signature schemes are provably secure in the random oracle model or the weak models without random oracles such as gauntlet-ID model. Currently, there is no hierarchical identity based signature scheme that is fully secure in the standard model, with short public parameters and a tight reduction. In this paper, a hierarchical identity based signature scheme based on the q-SDH problem that is fully secure in the standard model is proposed. The signature size is independent of the level of the hierarchy. Moreover, our scheme has short public parameters, high efficiency and a tight reduction. Hierarchical identity based cryptography is a generalization of identity based encryption that mirrors an organizational hierarchy. It allows a root public key generator to distribute the workload by delegating public key generation and identity authentication to lower-level public key generators. Most hierarchical identity based signature schemes are provably secure in the random oracle model or the weak models without random oracles such as gauntlet-ID model. Currently, there is no hierarchical identity based signature scheme that is fully secure in the standard model, with short public parameters and a tight reduction. In this paper, a hierarchical identity based signature scheme based on the q-SDH problem that is fully secure in the standard model is proposed. Moreover, our scheme has short public parameters, high efficiency and a tight reduction.