In this study, we propose a new hybrid algorithm fusing the exploitation ability of the particle swarm optimization (PSO) with the exploration ability of the grey wolf optimizer (GWO). Our approach combines two methods by replacing a particle of the PSO with small possibility by a particle partially improved with the GWO. We have evaluated our approach on five different benchmark functions and on three different real-world problems, namely parameter estimation for frequency-modulated sound waves, process flowsheeting problem, and leather nesting problem (LNP). The LNP is one of the hard industrial problems, where two-dimensional irregular patterns are placed on two-dimensional irregular-shaped leather material such that a minimum amount of the material is wasted. In our evaluations, we compared our approach with the conventional PSO and GWO algorithms, artificial bee colony and social spider algorithm, and as well as with three different hybrid approaches of the PSO and GWO algorithms. Our experimental results reveal that our hybrid approach successfully merges the two algorithms and performs better than all methods employed in the comparisons. The results also indicate that our approach converges to more optimal solutions with fewer iterations.