Telecare Medicine Information Systems (TMIS) provides flexible and convenient healthcare for patients. However, the medical data transmitted between patients and doctors are exposed to unsecure public networks. To protect the patient’s personal information, many authentication schemes are designed. Recently, Kang et al. proposed a hash based authentication schemes for TMIS and claimed that it could resist various attacks. However, we find that their proposed scheme is unsecure to traceability attack and user impersonation attack. In order to enhance the security and preserve the efficiency of Kang et al.’s, we proposed a new anonymous and lightweight scheme. The analysis demonstrates that our proposed scheme is superior to Kang et al.’s and the related schemes in security.