How to make people keep both the confidentiality of the sensitive data and the privacy of their real identity in communication networks has been a hot topic in recent years. Researchers proposed privacy-preserving authenticated key exchange protocols (PPAKE) to answer this question. However, lots of PPAKE protocols need users to remember long secrets which are inconvenient for them. In this paper we propose a lightweight three-party privacy-preserving authentication key exchange (3PPAKE) protocol using smart card to address the problem. The advantages of the new 3PPAKE protocol are: 1. The only secrets that the users need to remember in the authentication are their short passwords; 2. Both of the users can negotiate a common key and keep their identity privacy, i.e., providing anonymity for both users in the communication; 3. It enjoys better performance in terms of computation cost and security. The security of the scheme is given in the random oracle model. To the best of our knowledge, the new protocol is the first provably secure authentication protocol which provides anonymity for both users in the three-party setting.