The laser induced air-breakdown and propagation mechanism of laser sustained plasma detonation (LSD) were analyzed in detail. Based on Navier-Stokes equations, the analysis models considering turbulence and plasma irradiation were established for flow field. And the evolvement of plasma shock wave in thruster was systematically analyzed by the finite volume method. The effects of single pulse energy and width on propulsion performance were described also. The production and transmission process of Mach cone observed in many experiments has been captured in this numerical simulation. The relation between thrust, impulse coupling coefficient and one pulse laser energy, pulse width were gained, which agreed well with the experimental results by Germany Space Center. These numerical results can provide some reference for the pulse laser choice and pulse parameters optimization.