An undeniable mobile billing system allows a mobile network service provider to bill its subscribers with trustworthy evidences. Chen, Jan and Chen proposed such a billing system by introducing a trusted third party – Observer and exploiting a hash chain mechanism. In their system, the Observer provides call time evidence to both cellular carriers and subscribers for billing. In this paper, we first identify some vulnerabilities in their mobile billing system. Then, we propose an undeniable billing scheme based on a proper combination of digital signature and hash chain mechanism. The proposed scheme can achieve authentication, non-repudiation, and fairness, which are desirable security requirements for an undeniable mobile billing system.