Cold spray has recently emerged as a promising new technology for various coating, additive manufacturing, and on-site repair needs. One key challenge underlying cold spray is the proper simulation of the deposition process, for which numerous numerical studies have been carried out, but often fail to consider the interfacial adhesion. In this study, a new numerical approach on the base of peridynamics (PD) was developed to incorporate interfacial interactions as a part of the constitutive model to capture deformation, bonding, and rebound of impacting particles in one unified framework. Two models were proposed to characterize the adhesive contacts, i.e., a long-range Lenard-Johns type potential and a force-stretch relation of the interface directly derived from fracture properties of the bulk material. Using copper as the sample material, the deformation behaviors simulated by the PD-based approach were found to compare well with those from benchmark finite element method simulations. It was further demonstrated that this PD-based approach allows flexibility to realize different deposition scenarios, such as particle-substrate bonding and separation, by modulating adhesion energies. The approach provides a new numerical framework for more realistic cold spray impact simulations.