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Key agreement protocols are a fundamental building block of cryptography to establish a common secret key over public network. We propose an efficient and secure three-pass authenticated key agreement protocol based on elliptic curve where three-pass protocols have significant advantages over two-pass in terms of security properties and applications. The three-pass protocols can prevent denial of service attacks in complex and unpredictable communication environments such as wireless networks and Internet. We show the proposed protocol can withstand a stronger adversary under eCK security model by using a trick in its block of hashing a static secret key with an ephemeral secret key. Furthermore, it can provide an assurance of the identity authentication of its partner, thus it can withstand non-repudiation attacks. Therefore, it is suitable for electronic commerce to provide non-repudiation services. By comparing the security and computational complexity of the proposed protocol with other existing protocols in our study, we show that the proposed protocol not only satisfies all security attributes but also obtains computational efficiency with a cost of 3 point multiplications.