Abstract: A projected wave function approach based on projection operators in the form of matrix-product operators is introduced. This approach allows us to variationally improve the short-range entanglement of a given trial wave function while the long-range entanglement is contained in the initial guess. We demonstrate the feasibility of the approach by considering a one-dimensional model of interacting spinless fermions. In addition, we indicate how to generalize this approach to higher dimensions using projection operators based on tensor products.