For multi-dimensional and huge amount calculations, an approximate model with sufficient accuracy and fast calculation speed for the variable geometry supersonic inlet with large Mach number range is needed urgently. To solve the convergence at partial-best point of current quantum-particle swarm optimization Kriging approximate model, the global criterion improved quantum-behaved particle swarm optimization is presented, which is validated with high precision, fast speed and strong adaption to high non-linear function by rebuilding two test functions. The approximate model of variable geometry supersonic inlets with 2~4 Mach number range is established by 5 variable parameters: Ma, angle of attack, horizontal displacement of cowl, second inlet ramp angle and its displacement. The application of the presented model method is validated with high accuracy and adaptability.