The present study aimed to investigate the intrinsic reaction of hydrodesulfurization (HDS) for a real Straight Run Heavy Naphtha (SRHN) over CoMo-S/Al2O3 catalyst in a fixed- bed reactor. Influence of the process parameters on sulfur removal was investigated by regulating the temperature (T = 320-380 oC), pressure (P = 20 to 35 bar), weight hour space velocity (WHSV = 2.5 to 5.0 h-1) and catalyst average particle size (dp =361 to 3950 μm). Mears and Weisz-Prater criteria were estimated and utilized to validate the intrinsic reaction condition. Operating variables were optimized at (T = 360 oC, P = 30 bars, WHSV = 2.5 h-1, dp= 361 μm) to obtain an optimum sulfur removal of 93.4% under intrinsic reaction conditions. Experimental results showed that % activity of sulfur removal increases to 93.4% as temperature increased to 360oC but it reduces to 90.3% as space velocity increased to 5.0 h-1. Kinetic parameters of the intrinsic reaction rate were estimated and compared with published data. Long-time test was performed on the sulfided catalyst to investigate its activity.