In recent years, wireless technology has gained popularity due to its cost effectiveness when compared to wired network. On the other hand, it is open to security attacks because of its transmission media. Out of various security issues related to wireless network, authentication is the primary one. To accomplish this, password based smart card authentication scheme is the most prominent scheme. However, most of these schemes are vulnerable to one or the other possible attacks. This paper presents an efficient and secure smart card authentication scheme based on difficulty in solving Elliptic Curve Discrete logarithm Problem (ECDLP). It allows users to choose and change the password without taking any assistance from the Home Agent (HA). Security analysis proves that the proposed scheme is more secure and practical.