Slime mould algorithm (SMA) has shortcomings in handling global optimization problems such as its slow convergence speed and low solution accuracy. To overcome the shortcomings of SMA, in this study a new improved slime mould algorithm with the Cauchy mutation (CM) is proposed, named as (CMSMA). The Cauchy mutation is applied to the best position of slime mould to boost the local search ability of the algorithm and to avoid being trapped in a local optimal. The performance of the CMSMA algorithm is evaluated by optimizing one of the complex mechanical engineering design problems, i.e., four-stage gear box (FSGB) problem. The outcomes of CMSMA are compared with the other state-of-art algorithms, the CMSMA performs better for finding the most optimal design for the given mechanical engineering design problem.