The smart grid (SG) is seen as a possible solution to the energy crises and carbon emissions. The power consumption data is collected through SG communication in order to optimize energy usage. Security problems in smart grid communications on the other hand continue to be virtual concerns. Various key agreement and authentication systems have recently been proposed in the context of SG communication in order to protect the users privacy and provide secure communication. Mood and Nikooghadam published a paper entitled Anonymous ECC-Based Self-Certified Key Distribution Scheme for Smart Grid in IEEE Transactions on Industrial Electronics [https://doi.org/10.1109/TIE.2018.2807383]. In this proposed work, we analyze Mood and Nikooghadam protocol and found security flaws such as the inability to protect anonymity, fails user traceability, DoS attack, insider attack, no updating the identity and keys and no login phase. Thus, Mood and Nikooghadam protocol is not convenient for smart grid communication. Further, we provide suggested improvement for Mood and Nikooghadam framework.