Three-party password authenticated key exchange (3PAKE) protocols allow two clients to establish a common session key via the help of an authentication server. Each client only needs to share a password with the server. The derived session key can be later used to achieve end-to-end secure communications. Most of the existing 3PAKE protocols are proven secure in the random oracle model. However, these protocols may turn out to be insecure in real applications when the random oracle function is instantiated with a concrete hash function. In this paper, an efficient 3PAKE protocol is proposed using smooth projective hash function based on ElGamal public key encryption. The security of the proposed protocol is conducted in the standard model under the DDH assumption. Compared with other related protocols, this protocol is quite efficient in terms of computation and communication costs under the same security assumption, and as a result, it is more suitable for large-scale end-to-end communication environments.