In real-life applications, ensuring secure transmission of data over public network channels to prevent malicious eavesdropping of the data is an important issue. Several potential security risks arise while protecting data and providing access control over the data. Due to the broadcast nature of the wireless channels, wireless networks are often vulnerable to various possible known attacks. Therefore, designing a secure and efficient authentication scheme in the global mobility network (GLOMONET) environment becomes a challenging task to the researchers. In recent years, several user authentication schemes for roaming services in GLOMONET have been proposed. However, most of them are either vulnerable to various known attacks or they are inefficient. Most recently, Zhao et al. proposed an anonymous authentication scheme for roaming service in GLOMONET (Zhao et al. in Wireless Personal Communications 78:247–269, 2014) and they claimed that their scheme can withstand all possible known attacks. In this paper, Zhao et al.’s scheme is revisited, and it is shown that their scheme fails to provide strong user anonymity when the session-specific temporary information are revealed to an adversary. Further, their scheme does not protect replay attack, offline password guessing attack and privileged-insider attack. In addition, there is no provision for revocation and re-registration mechanism in their scheme and also there exists design flaw in their schemeu. Moreover, another recently proposed Memon et al.’s scheme (Memon et al. in Wireless Personal Communications 84:1487–1508, 2015) fails to protect the privileged-insider attack. Thus, there is a great need to provide security enhancement of their schemes in order to apply in practical applications. The proposed scheme withstands the security weaknesses found in Zhao et al.’s scheme and Memon et al.’s scheme. Through the rigorous formal and informal security analysis, it is shown that the proposed scheme has the ability to tolerate various known attacks. In addition, the proposed scheme is simulated using the most-widely accepted and used Automated Validation of Internet Security Protocols and Applications tool and the simulation results reveal that the proposed scheme is secure. The proposed scheme is also efficient in computation and communication as compared to Zhao et al.’s scheme and other related schemes.