A deterministic algorithm is developed to implement a physical-based gas-surface interaction model. The key of the algorithm is to calculate discretized matrix by a deterministic way, which represents the scattering kernel of single gas-surface collision and governs the gas molecular velocity distribution function.By considering the attractive potential well and successive gas-surface collisions, this algorithm describes physically the variation of gas molecular velocity distribution functions at the interface.Comparing with existing stochastic implementation algorithm based on Monte Carlo sampling, this deterministic implementation algorithm calculates accurately and efficiently the relation between incident and reflected velocity distributions of gas molecules. Therefore, it provides a better boundary condition for the deterministic simulation methods of rarefied gas flows based on discretized velocity space.