In this article, an improved variant of the grey wolf optimizer (GWO) named gaze cues learning-based grey wolf optimizer (GGWO) is proposed. The main intentions are to reduce the existing high selective pressure and low diversification of the GWO algorithm, which results in premature convergence, local optima trapping, and stagnation problems. The GGWO algorithm benefits from two new search strategies: neighbor gaze cues learning (NGCL) and random gaze cues learning (RGCL) inspired by the gaze cueing behavior in wolves. The NGCL strategy enhances the exploitation ability and local optima avoidance. The RGCL, however, boosts the population diversity and balance between exploration and exploitation. The cooperation among three search strategies GWO, NGCL, and RGCL, improves diversification, exploration, and exploitation. The GGWO algorithm performance was evaluated by conducting CEC'18 test functions. Furthermore, the results of GGWO were compared with nine metaheuristic algorithms KH, iwPSO, WOA, GWO, GWO-EPD, HGWOSCA, EEGWO, BOA, and VAGWO. Moreover, the experimental results were statistically analyzed by the Wilcoxon signed-rank and Friedman tests. Additionally, four real engineering design problems and two problems of optimal power flow (OPF) for the IEEE 30-bus and IEEE 118-bus are optimized to verify the applicability of the GGWO in practice. The results show that the GGWO algorithm has been able to provide competitive and superior results to the compared algorithms, and it is capable of solving engineering problems.