Laser cutting is a popular manufacturing process utilized to cut various types of materials. There are many non-linear interaction factors responsible for the performance of the laser cutting process. Identification of dominant factors that significantly affect cut quality is important. In this paper, the effect of the process parameters is analysed on the laser cut quality of an uncommon alloy, the tungsten alloy sheet with thickness of 1 mm. The experiments are conducted at three levels of the selected process parameters such as assist gas type (oxygen, air and nitrogen) and assist gas pressure. Taguchi design of experiments is used to obtain the optimum conditions through the study of signal to noise ratio for three quality characteristics such as kerf width, heat affected zone and surface roughness. Results of this study indicate that the optimal assist gas pressure is entirely different for kerf width, heat affected zone and surface roughness. The nitrogen as assist gas is suggested as the optimal assist gas for all of three quality characteristics.