Recently established Harris hawks optimization (HHO) has natural behavior for finding an optimum solution in global search space without getting trapped in previous convergence. However, the exploitation phase of the current Harris hawks optimizer algorithm is poor. In the present research, an improved version of the HHO algorithm, which combines Harris hawks optimizer with Canis lupus inspire grey wolf optimizer (GWO) and named as hHHO-GWO algorithm, has been proposed to find the solution of various optimization problems such as nonlinear, nonconvex, and highly constrained engineering design problem. In the proposed research, the phase of exploration and exploitation of the existing HHO algorithm has been further improved using GWO algorithm and its performance has been tested for various benchmarks problems including CEC2005 (unimodal, multimodal, and fixed dimensions functions), multimodal functions with variable dimensions, and CEC-BC-2017 test functions. Further, the developed hybrid optimizer has been tested for 11 different engineering design and optimization problems and experimental results of hHHO-GWO have been compared with other optimizer.