In three-party authenticated key exchange protocols, each client shares a secret only with a trusted server with assists in generating a session key used for securely sending messages between two communication clients. Compared with two-party authenticated key exchange protocols where each pair of parties must share a secret with each other, a three-party protocol does not cause any key management problem for the parties. In the literature, mainly there exist three issues in three-party authenticated key exchange protocols are discussed that need to be further improved: (1) to reduce latency, communication steps in the protocol should be as parallel as possible; (2) as the existence of a security-sensitive table on the server side may cause the server to become compromised, the table should be removed; (3) resources required for computation should be as few as possible to avoid the protocol to become an efficiency bottleneck. In various applications over networks, a quick response is required especially by light-weight clients in the mobile e-commerce. In this paper, a round- and computation-efficient three-party authenticated key exchange protocol is proposed which fulfils all of the above mentioned requirements.