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.