In some scenes such as smart mobile terminal, low energy consumption and high efficiency are highly important in information security. So two-factor authentication scheme based on classical encryption algorithms are not suitable in some scenes. Negative database (NDB), inspired by the artificial immune system, is significant with wide applications in information security and privacy protection for the high efficiency. Password authentication schemes based on NDBs can be used in mobile internet, sensor network and smart card because of the high efficiency of generating NDBs. This paper proposes a two-factor authentication scheme based on NDBs, the security of the scheme depends on the NP-Completeness of reversing an NDB to obtain the original database (DB). The efficiency of this proposed scheme is similar to the present one-time password authentication scheme based on NDBs. The efficiency and the security of this proposed scheme is analyzed as well.