Recently, several studies about proxy signature schemes have been conducted. In 2009, Yu et al. proposed an anonymous proxy signature scheme attempting to protect the proxy signer's privacy from outsiders. They claimed that their scheme can make the proxy signer anonymous. However, based on our research, we determined that this was not the case and the proxy signer's privacy was not anonymous. Hence, in this paper, we propose a new anonymous proxy signature scheme that truly makes the proxy signer anonymous while making it more secure and efficient when compared with Yu et al.'s scheme. Our proxy signature scheme consists of two contributions. First, we mainly use random numbers and bilinear pairings to attain the anonymous property. Secondly, we increase the security and efficiency of our proxy in the design.