We present a Lattice Boltzmann model to simulate compressible flows by introducing an attractive potential 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 greatly(up to more than 3). Simulations of March cone and the comparison between theoretical expectations and simulations demonstrate that the scheme is effective in simulation of compressible flows with high Mach numbers, which would open many new applications.