Nowadays, remote user authentication protocol plays a great role in ensuring the security of data transmission and protecting the privacy of users for various network services. In this study, we discover two recently introduced anonymous authentication schemes are not as secure as they claimed, by demonstrating they suffer from offline password guessing attack, desynchronization attack, session key disclosure attack, failure to achieve user anonymity, or forward secrecy. Besides, we reveal two environment‐specific authentication schemes have weaknesses like impersonation attack. To eliminate the security vulnerabilities of existing schemes, we propose an improved authentication scheme based on elliptic curve cryptosystem. We use BAN logic and heuristic analysis to prove our scheme provides perfect security attributes and is resistant to known attacks. In addition, the security and performance comparison show that our scheme is superior with better security and low computation and communication cost.