Many identity-based proxy signature (IBPS) schemes have been proposed, but most were proved to be secure using a random oracle model, which has attracted considerable criticism. Cao and Cao proposed an IBPS scheme using the standard model, but their scheme was shown to be insecure because it could not resist a delegator attack. In order to overcome this weakness, Gu et al. proposed a new IBPS scheme in 2013 that uses the standard model and they also provided a detailed security model for IBPS. However, in this study, we demonstrate that Gu et al.'s scheme is still vulnerable to delegator attack. In order to correct this problem, we propose an improvement of the IBPS scheme described by Gu et al. We also present an efficiency analysis for our scheme and a detailed security proof based on the computational Diffie-Hellman assumption.