Fixed point theory and contractive mappings are popular tools in solving a variety of problems such as control theory, economic theory, nonlinear analysis, and global analysis. There are many works on different types of contractions to find a fixed point in metric spaces. Improving and extending some of those, in this paper, we introduce a new version of $H$-contraction for four mappings in a metric space $(X,d)$. Then, we prove the existence and uniqueness of a common best proximity point for four non-self mappings. An example is also given to support our main result. The related fixed point theorem is also proved.