In three-party password authenticated key exchange(AKE) protocol, since two users use their passwords to establish a secure session key over an insecure communication channel with the help of the trusted server, such a protocol may suffer the password guessing attacks and the server has to maintain the password table. To eliminate the shortages of passwordbased AKE protocol, very recently, according to chaotic maps, Lee et al. [2015 Nonlinear Dyn. 79 2485] proposed a first three-party-authenticated key exchange scheme without using passwords, and claimed its security by providing a wellorganized BAN logic test. Unfortunately, their protocol cannot resist impersonation attack, which is demonstrated in the present paper. To overcome their security weakness, by using chaotic maps, we propose a biometrics-based anonymous three-party AKE protocol with the same advantages. Further, we use the pi calculus-based formal verification tool Pro Verif to show that our AKE protocol achieves authentication, security and anonymity, and an acceptable efficiency. In three-party password authenticated key exchange (AKE) protocol, since two users use their passwords to establish a secure session key over an insecure communication channel with the help of the trusted server, such a protocol may suffer the password guessing attacks and the server has to maintain the password table. To eliminate the shortages of password based on AKE protocol, very recently, according to chaotic maps, Lee et al. [2015 Nonlinear Dyn. 79 2485] proposed a first three-party-authenticated key exchange scheme without using passwords , and claimed its security by providing a wellorganized BAN logic test. Unfortunately, their protocol can not resist impersonation attack, which is demonstrated in the present paper. To overcome their security weakness, by using chaotic maps, we propose a biometrics-based anonymous three- party, AKE protocol with the same advantages. Further, we use the pi calculus-based formal verification tool Pro Verif to show that our our AKE protocol achieves authenti cation, security and anonymity, and an acceptable efficiency.