In 2010, Fan et al. proposed an efficient anonymous multi-receiver identity-based encryption scheme. This scheme allows a sender to send an encrypted message to a set of designated receivers while preserving receiver anonymity. The scheme is highly efficient for each receiver as it requires only two pairing operations. However, we found that the scheme failed to protect receiver anonymity and the security notation for receiver anonymity captures only semantics in the case of a single receiver, but does not for multiple recipients. In this paper, we present the weaknesses and propose an improved scheme. The improved scheme enhances both security and computational performance.