Laser propulsion powered by a CW laser has been studied. Thruster performance and energy balance in the thruster were numerically computed. Laser beam optics, inverse-bremsstrahlung absorption, ionization/recombination reactions, radiation, heat conduction, and convection have been modeled. Computational stiffness resulting from the very small flow speed has been overcome by using a flux vector splitting implicit scheme with a large CFL number. The computed positions of the Laser Sustained Plasma (LSP) in the thruster show good agreement with the measured ones. The estimated energy conversion efficiency was 23%, and the rest of the input power was lost as radiation from the LSP and also carried by the laser beam passing through the LSP.