Abstract: A simple two-dimensional lattice Boltzmann model with three speeds is studied. The local equilibrium distribution functions are determined under the restrained conditions of fluid dynamics by connecting the discrete model with the continuum macro-models. Euler equation and Navier-tokes equation are derived by using Chapman-Enskog expansion and multi-scalar technique, and the viscosity formula is also provided.The model has been applied to cavity flow problem with satisfactory results.