Harris Hawks optimization (HHO) is a recently introduced meta-heuristic approach, which simulates the cooperative behavior of Harris’ hawks in nature. In this paper, an improved variant of HHO is proposed, called HHSC, to relieve the main shortcomings of the conventional method that converges either fast or slow and falls in the local optima trap when dealing with complex problems. Two search strategies are added into the conventional HHO. First, the sine function is used to improve the convergence speed of the HHO algorithm. Second, the cosine function is used to enhance the ability of the exploration and exploitation searches during the early and later stages, respectively. The incorporated new two search methods significantly enhanced the convergence behavior and the searchability of the original algorithm. The performance of the proposed HHSC method is comprehensively investigated and analyzed using (1) twenty-three classical benchmark functions such as unimodal, multi-modal, and fixed multi-modal, (2) ten IEEE CEC2019 benchmark functions, and (3) five common engineering design problems. The experimental results proved that the search strategies of HHO and its convergence behavior are significantly developed. The proposed HHSC achieved promising results, and it got better effectiveness in comparisons with other well-known optimization methods.