In edge computing, the task offloading balance effectively, adaptability and reliability which aims to enhance the resource utilization, enhance the user experience while considering dynamic and limited resource. The Meerkat Clan Algorithm with Chaotic Map and Crossover Strategy (MCA-CC) is proposed in this research for energy-aware computation offloading in edge computing. The MCA-CC improves the exploration ability of the algorithm by adding chaotic maps, thus reducing the possibility of early convergence to a local solution. Chaotic maps bring in non-linear randomness into the search space and this enhances the utilization of several solution spaces efficiently. This feature is most useful when the search space is multimodal or has a non-convex shape when global optimum is difficult to locate. The crossover strategy helps in creating better inherited solutions and makes a switch to better solutions faster in the given problem space. Also, crossover is applied with chaotic map making it possible to enhance the level of exploration without compromising on the exploitation and to avoid trapping in exploitation suboptimal areas. The MCA-CC obtains execution time of 530 s, energy consumption (EC) of 85 mJ and service cost of 195$ which is better than state-of-art approaches.