Underground coal mines are considered as one of the most dangerous workspaces as many hazardous factors regularly cause accidents. It may be avoided by real-time monitoring of environmental parameters (gas, temperature, the width of walls, etc.) of underground tunnels. Nowadays, wireless sensor network (WSN) is widely used for safety monitoring of coal mines. However, any kind of interception, modification and interruption of transmission of environmental parameters can mislead the professionals that might lead to amajor accident. Therefore, security is an essential issue for WSN-based safety monitoring. Sensors in WSN have limited computational power and storage capacity, which creates a challenge to design authentication and keyagreement (AKA) scheme with low computational cost. To address these issues, As this scheme is light-weight and provides mutual authentication (MA), sensor anonymity (SA) and user anonymity (UA), we have considered this scheme for a case study. We first propose the cryptanalysis of this scheme, in which we prove that this scheme fails to resist sensor node compromise (SNC), stolen smart card (SSC) and user impersonation (UI) attacks. To counteract these attacks and to provide efficient authentication scheme, we propose a lightweight AKA scheme for WSN-based safety monitoring in coal mines. We simulated the scheme on AVISPA tool. We used the random oracle model (ROM) to perform formal security analysis and also performed informal security analysis. These analyses demonstrate that the proposed scheme is secure and invulnerable to various known attacks. We compared the proposed scheme to other related schemes regarding security features and computational cost. Our scheme requires comparable computational cost and is more secure than related schemes.