At present, most existing key exchange protocols for three-party (3pake) are easily attacked by server key disclosure, dictionary attack and so on. This paper analyses the weakness of the previous work , and presents a key exchange for three-party based on the private key .This method can resist common attack through safety analysis, and the efficiency analysis result shows its efficiency. On the basis of the new 3pake, a cross-realm key exchange protocol (c2c-pake) will be also presented, the new c2c-pake only needs 3 rounds to make users generate a common session key without asymmetric or symmetric encryption, and it can be proved safe through safety analysis.