We propose a conservative and entropic discrete-velocity method to compute the solutions of the Boltzmann equation in the case of monoatomic species. We begin by defining a discrete collision kernel on a velocity lattice verifies all the properties of the continuous kernel. The continuous Boltzmann equation will be replaced by a Boltzmann equation for a discrete velocity gas, which is a hyperbolic system. This equation will be discretize by a finite volume scheme. For the evaluation of the collision term we use acceleration procedures of Monte Carlo type. The possibilities of our scheme will be illustrate by numerical tests in 1 and 2 space dimensions.