Cloud computing is a service-oriented architecture, which has a pool of resources. This paper introduces the resource allocation scheme for cloud computing by introducing an optimisation algorithm named Chronological E-Lion algorithm. The proposed Chronological E-Lion algorithm is developed by integrating the chronological concept to the EWMA-based Lion algorithm. The fitness function of the proposed Chronological E-Lion algorithm considers various parameters, like cost, profit, CPU allocation, memory allocation, MIPS, and frequency scaling, for optimally allocating the resources. The performance of the proposed method is analysed using three different problem instances based on the evaluation metrics, profit, CPU allocation rate, and memory allocation rate. From the simulation results, it can be concluded that the proposed Chronological E-Lion algorithm achieved improved performance with the values of 45.93, 0.16, and 0.0093, for profit, CPU utilisation rate, and memory utilisation rate. © 2020 Inderscience Enterprises Ltd.