Abstract: A new adaptive lattice Boltzmann model is presented to simulate super-sonic flows. Particle velocities may have a large range of values. The support set of equilibrium distributions is determined by the mean velocity and internal energy. The adaptive nature of particle velocities permit the mean flow to have a high Mach number. A particle potential energy is introduced to make the model suitable for the perfect gas with arbitrary specific heat ratio. Navier-Stokes equations are derived by the Chapman-Enskog method from the BGK Boltzmann equation. As numerical test, the simulation is performed for a flow passing over a forward-facing step at Mach number 3 on a hexagonal lattice. The shocks are well captured.