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In the internet banking environment, using credit cards to pay the services is one of the most popular and simplest methods. However, this is dangerous if users information or smart-card is stolen. With a non-stop development of mobile and wearable devices, user authentication scheme which is security and low-resource efficient is a subject of interest. Modern devices help securing login phase by exploit biometrics collecting from them. Recently, Saru Kumari et al. proposed a remote scheme with key agreement to overcome popular kinds of attacks. However, in this paper, we realize their scheme is still vulnerable to two-factor attack and does not achieve user anonymity. In addition to security analysis, we presented an improved scheme to have a better solution with elliptic curve cryptosystem.