Abstract-In a designated verifier signature scheme, only the designated person can verify the validity of the signature. Due to such attribute, it could be used in many fields such as financial payment system, e-voting, and e-taxation. Recently, Lee et al. proposed an identity based signature scheme to overcome weaknesses in previous schemes. In this paper, we will point out that Lee et al.'s scheme suffers from two kinds of attacks. To enhance security, an improved scheme will be also proposed. Security analysis shows that that the proposed scheme is provably secure in the random oracle model and could overcome weaknesses in Lee et al.'s scheme. Performance analysis demonstrates that our scheme could overcome weaknesses in Lee et al.'s weaknesses at the cost of increasing computational cost slightly.