Due to the rapid growth of the Industrial IoT (IIoT), social media and digitization, and wireless communication technology in various sectors, data volume is increasing rapidly. Cloud computing is an emerging solution with fog computing assistance for handling and processing a huge volume of data. It is a soar of means to improve the quality of services provided to users through cloud computing, which has been more overwhelmed by the massive data flow. Transmitting all the data to the cloud and getting it back from the cloud causes high latency and requires high network bandwidth. In the IIoT applications, there is enough energy needed in the fog layer, a promising area to be handled by the cloud service providers. An important factor that contributes to the energy consumption in fog servers is VM allocation. This paper proposes EVMAS, i.e., an energy-aware VM allocation scheme based on Lagrange’s undetermined multiplier with the Hessian matrix, which improves the Quality of Service (QoS) in parallel with service level agreement (SLA). The suggested technique outperforms in comparison to the other state of the algorithm.