The main objective of the present thesis is the exhibition of a modified model of standard Lattice Boltzmann method to simulate a compressible fluid flow. In this method, instead of limited velocity set for the particles, a large velocity set has been used. This velocity set are obtained from the addition of the mean velocity flow to lattice particle velocity which are determines the destination of fluid particles on the lattice nodes. The mentioned method in macroscopic level and a wide range of high Mach number, satisfies the continuum and N.S equations. Also, the ability of the mentioned method is increased by adding a suitable boundary condition for curved boundaries. Therefore, the possibility for simulating compressible fluid on airfoil is provided with appropriate accuracy.To investigate the capabilities of mentioned method, a computer program have been developed. In the next step, we applied this program to simulate some problems.In the first problem, the flow has been simulated over a wedge with supersonic velocity in order to show the ability of this method to make the oblique shock. In the second problem, the oblique shock reflection on an inviscid wall has been simulated. In this case, the wall do not coincide with any grid line. The numerical results have been compared with the similar problem which the wall was on grid lines. These results confirm the appropriate choosing of the boundary condition for curved boundary.Finally in order to show other abilities of this method, the flow over a NACA0012 airfoil with different boundary conditions has been simulated. In the first problem of this case viscous flow with has been simulated. The numerical results showed that this method has a good accuracy to simulate these problems. .Key Words.Lattice boltzmann, Compressible flow, Curve boundary, Shock