The utilization of composite materials has nowadays increased in aerospace applications due to their less weight and superior mechanical properties. Nevertheless, machining of composite materials without damage is quite challenging through conventional system due to their inherent heterogeneity, anisotropy, and thermal sensitivity. To overcome this problem, abrasive water jet machining process can be employed. It is a non-conventional machining processes with high accuracy, high flexibility and with no heat generation. However, there are more challenges in cutting fiber reinforced plastics with this technique. Hence, this work deals with the assessment of the optimum process parameters in abrasive water jet cutting of carbon fiber reinforced plastic composite. Cutting experiments were conducted by varying input parameters such as the traverse rate, standoff distance on three laminates of different thickness. Analysis of variance through response surface methodology technique was used to study the effect of each input parameters on the output responses such as kerf taper and surface roughness. Optimum parameters that provide the best machining quality were found using numerical and graphical optimization techniques. The results showed that increasing the traverse rate results in increased surface roughness and taper angle of the cut kerf. Hence lower traverse rate is preferable when machining quality is of high importance.