Focused on the issues of high communication rounds and low execution efficiency in existing lattice-based three-party Password-Authenticated Key Exchange （PAKE） protocols， a two-round three-party PAKE protocol over lattices without Non-Interactive Zero-Knowledge （NIZK） proof was proposed. First， the advantage of non-adaptive approximate smooth projective hash function was taken to achieve key exchange and reduce the number of communication rounds without NIZK proof. Second， session keys were constructed by using hash values and projection hash values without random oracles， thus avoiding potential password guessing attacks. Finally， formal security proof of the proposed protocol was given in the standard model. Simulation results show that compared with lattice-based three-party PAKE protocols， the proposed protocol has the execution time reduced by 89.2% - 98.6% on the client side and 19.0% - 91.6% on the server side. It is verified that the proposed protocol can resist quantum attacks with high execution efficiency and few communication rounds.