With the rapid development of personal information and wireless communication technology, user authentication schemes have been crucial to ensure that wireless communications are secure. As such, various authentication schemes with multi-factor authentication have been proposed to improve the security of electronic communications. Multi-factor authentication involves the use of passwords, smart cards, and various biometrics to provide users with the utmost privacy and data protection. Cao and Ge analyzed various authentication schemes and found that Younghwa An’s scheme was susceptible to a replay attack where an adversary masquerades as a legal server and a user masquerading attack where user anonymity is not provided, allowing an adversary to execute a password change process by intercepting the user’s ID during login. Cao and Ge improved upon Younghwa An’s scheme, but various security problems remained. This study demonstrates that Cao and Ge’s scheme is susceptible to a biometric recognition error, slow wrong password detection, off-line password attack, user impersonation attack, ID guessing attack, a DoS attack, and that their scheme cannot provide session key agreement. Then, to address all weaknesses identified in Cao and Ge’s scheme, this study proposes a security enhanced multi-factor biometric authentication scheme and provides a security analysis and formal analysis using Burrows-Abadi-Needham logic. Finally, the efficiency analysis reveals that the proposed scheme can protect against several possible types of attacks with only a slightly high computational cost.