In order to access remote medical server, generally the patients utilize smart card to login to the server. It has been observed that most of the user (patient) authentication protocols suffer from smart card stolen attack that means the attacker can mount several common attacks after extracting smart card information. Recently, Lu et al.'s proposes a session key agreement protocol between the patient and remote medical server and claims that the same protocol is secure against relevant security attacks. However, this paper presents several security attacks on Lu et al.'s protocol such as identity trace attack, new smart card issue attack, patient impersonation attack and medical server impersonation attack. In order to fix the mentioned security pitfalls including smart card stolen attack, this paper proposes an efficient remote mutual authentication protocol using smart card. We have then simulated the proposed protocol using widely-accepted AVISPA simulation tool whose results make certain that the same protocol is secure against active and passive attacks including replay and man-in-the-middle attacks. Moreover, the rigorous security analysis proves that the proposed protocol provides strong security protection on the relevant security attacks including smart card stolen attack. We compare the proposed scheme with several related schemes in terms of computation cost and communication cost as well as security functionalities. It has been observed that the proposed scheme is comparatively better than related existing schemes.