This paper aims at establishing the existence and uniqueness of solutions for a nonstandard variational-hemivariational inequality. The solutions of this inequality are discussed in a subset K of a reexive Banach space X. Firstly, we prove the existence of solutions in the case of bounded closed and convex subsets. Secondly, we also prove the case when K is compact convex subsets. Finally, we enhance the main results by the application of some differential inclusions.