The conservation of energy in flying ad-hoc networks (FANETs) is a crucial issue that needs to be addressed to make clustering efficient and effective for these networks. However, selecting energy-efficient cluster heads (CHs) is vital for optimal clustering. Improperly chosen CHs can lead to excessive energy consumption during data transmission. It reduces network lifetime and overall performance. To address these challenges, we have developed a new algorithm for selecting the cluster head for UAVs using grey wolf optimization called CH-GWO (Cluster Head through Grey Wolf Optimization). We have proposed an objective function and weight parameters to facilitate efficient cluster head selection and formation. The proposed CH-GWO protocol is extensively analyzed in this research using the MATLAB 2021b environment for simulation. It enables us to evaluate its performance against other well-known clustering algorithms, namely K-means, low-energy adaptive clustering hierarchy (LEACH), hybrid energy-efficient distributed clustering (HEED), distributed energy-efficient clustering (DEEC), enhanced energy-efficient unequal clustering (EEUC), and stable election protocol (SEP). The results demonstrate that the CH-GWO algorithm significantly enhances the network lifetime by 20%, 18.9%, 14.8%, 12.5%, 7.8%, and 3.8% compared to K-means, LEACH, HEED, DEEC, EEUC, and SEP, respectively. As a result of the proposed method, the average energy consumption of the system is reduced by 37.5%, 33.3%, 29.78%, 19.7%, 16.6%, and 6.25% compared to the conventional algorithms. Based on the experimental data obtained through simulations, the CH-GWO algorithm outperforms K-means, LEACH, HEED, DEEC, EEUC, and SEP in various performance metrics, including network lifetime, packet delivery ratio, throughput, bit error rate (BER), time analysis, and end-to-end delay. These findings establish the effectiveness and superiority of the CH-GWO algorithm for cluster head selection in FANETs.