Propulsion of a space vehicle by means of a laser beam is among several innovative propulsion concepts currently being studied, The main advantage gained is the low-weight system, from decoupling the energy source from the space vehicle, and the low fuel consumption, thus achieving high levels of thrust and specific impulse, This paper concerns the design of a Laser propulsion system based on the repetitively pulsed method, while taking into consideration the relevant physical processes occurring inside the engine, namely, inverse bremsstrahlung and the laser detonation wave, A feasibility study was conducted for a Hohmann orbital transfer, using an engine with a parabolic nozzle that focuses a projected laser beam to its focal region, enabling gas ionization and plasma ignition. The focusing of the laser beam was studied according to the ray-tracing technique, Mathematical simulation was applied to investigate the effect of the nozzle wall roughness to determine the sensitivity of laser intensity distribution within the focal region (and hence the size of the preliminary ionized volume) to nozzle surface quality, Results show that for elevating a satellite weighing 500 kg from 300 to 36,000 km above Earth, a suitable engine can be designed, producing 19,600 N with I-sp of 1200 s, A laser power of 400 MW is required to perform the maneuver, with 10,000 pulses per second of 30-ns duration at an energy level of about 50 kJ per pulse.