A proxy signature scheme allows an entity to delegate his signing capabilities to another. Many schemes have been provided for use in numerous applications such as distributed computing, grid computing, and mobile communications. In 2003, Boldyreva et al. introduced the first formal security model of proxy signatures and also proposed a generic construction secure in their model. However, an adversary can arbitrarily alter the warrants of the proxy signatures because the warrants are not explicitly considered in their model. To solve this problem, Huang et al. provided an enhanced security model of proxy signatures in 2005. Some proxy signatures secure in this security model have been proposed but there is no generic construction yet. In this paper, we redefine and improve the Huang et al.'s security model in terms of multi-user and then provide a new generic construction of proxy signatures secure against our enhanced security model based on ID-based signatures. Moreover, we can make a lattice-based proxy signature scheme in the standard model from our result.