Abstract: The authors present a LB model to simulate high Mach-number flows by introducing an attractive force based on the simple selectable sound speed model. The corresponding macro-dynamical equation from Chapman-Enskog expansion shows that this model has the advantage to soften sound speed effectively and then the Mach-number is raised greafly(up to more than 5); The establishment of the model will open the wide vista in simulating high Mach-number flows by means of lattice.