In this paper we are interested in a dynamic description of the collective pedestrian motion based on the kinetic model of Bathnagar-Gross-Krook (BGK). In this model a pedestrians trend towards a state of equilibrium in a certain relaxation time is modeled. An approximation of the Maxwellian function that represents this equilibrium state is determined. A result of existence and uniqueness of the discrete velocity model is demonstrated. Thus the convergence of the solution to the solution of the continuous BGK equation is proven. Numerical tests are developed to validate the proposed mathematical model.