A numerical model is established for a continuous-wave laser-sustained plasma thruster which takes into consideration the chemical reactions, high-temperature thermodynamic properties, viscosity, diffusion, heat conduction and the effect of radiation on the thruster. The compressible axisymmetric Navier-Stokes equations are solved by pressure-based SIMPLEC algorithm. Given the same chamber pressure, beam focusing geometry and nozzle configuration, the specific impulses with argon propellant for different laser powers are calculated, as well as those with hydrogen for different throat radii. The results indicate that thruster with hydrogen has a better performance due to its intrinsic properties, and that properly reducing the thruster internal space can increase the specific enthalpy and heat uniformity of the propellant, thus improving the specific impulse.