In this study, the effect of cutting parameters on kerf quality and surface roughness in laser cutting of Al 5083 alloyed material was investigated both experimentally and statistically (Taguchi & Gray Taguchi). Experimental design was determined using the Taguchi L-18 (2(1)x 3(2)) orthogonal array. Experiments were carried out by using two different gas pressures (GP) (8 and 10 bar), three different cutting speeds (CS) (3500, 4000 and 4500mm.min(-1)) and laser power (P) (2600, 3100 and 3600W) in the cutting of Al 5083 alloyed material. As a result of the study, top kerf width (TKW), bottom kerf width (BKW) and average surface roughness (Ra) were measured as output parameter values. Using the measured top and BKW results, kerf taper (KT) was calculated. The lowest values of TKW, BKW, KT and Ra were 2.219mm, 2.010mm, 0.984 degrees and 2.394 mu m, respectively. To determine the optimum values of laser cutting parameters for minimum output parameters, signal-noise (S/N) ratio, variance and regression analysis, validity experiments and GRA methods were used. When S/N ratios were examined, the most ideal cutting parameters were determined as A(1)B(3)C(1) for TKW and BKW, A(2)B(1)C(3) for KT and A(2)B(3)C(3) for Ra. When the variance results were examined, it was determined that the most effective processing parameter for TKW, BKW and KT was at 46.04%, 50.58% and 56.45% CS, respectively, and the most effective processing parameter for Ra was laser power with 46.57%. According to gray relationship analysis, optimum laser cutting parameters for the smallest values of all output parameters were determined as A(1)B(3)C(1). According to gray relationship analysis, optimum laser cutting parameters for the smallest values of all output parameters were determined as A(1)B(3)C(1).