Recently, cold spray (CS) technology has attracted extensive interest as an alternative to thermal spray methods to build a coating, which uses high kinetic energy solid particles to impact and adhere to the substrate. To date, numerous numerical studies have been carried out to investigate the deposition processes and associated mechanisms during multiple particle impact in CS. However, in the commonly used numerical techniques, the individual powder particles are often treated separately from one another, thus fail to properly consider the adhesion mechanisms during deposition. In this study, we propose a new numerical approach on base of peridynamics (PD), which incorporates interfacial interactions as a part of constitutive model to capture deformation, bonding and rebound of impacting particles in one unified framework. Two models are proposed to characterize the adhesive contacts: a) a long-range Lenard-Johns type potential that reproduce the mode I fracture energy by suitable calibrations, and b) a force - stretch relation of interface directly derived from the bulk materials mode I fracture simulations. The particle deformation behavior modeled by the peridynamic method compares well with the benchmark finite element method results, which indicates the applicability of the peridynamic model for CS simulation. Furthermore, it is shown that the adhesive contact models can accurately describe interfacial bonding between the powder particles and substrate.