In 2004, Popescu proposed an efficient and secure key agreement protocol based on the Diffie-Hellman key agreement, which works in an elliptic curve group. The protocol, however, is still susceptible to a key-compromise impersonation attack, a reflection attack, and a replay attack. Accordingly, the current paper demonstrates the vulnerability of Popescu's protocol against such attacks and then an improved protocol is presented in order to resolve such problems.