In this present work, The effect of input parameters viz. grinding wheel speed, work-piece speed, abrasive grain size, depth of cut, concentration of cutting fluid, and number of passes has been found on the surface roughness of cylindrical grinded AISI 4140 steel has been found. The other parameters like feed rate, diameter of work-piece, coolant flow rate, etc. are kept constant. Three levels of each variable have been selected except wheel speed. Two levels of wheel speed have been taken. Heat treated AISI 4140 steel is selected as the work-piece material. The experiment is designed by using Taguchi's L18 orthogonal array. The effect of all the input parameters on the output responses have been analyzed using analysis of variance (ANOVA). The result reveals that depth of cut and work-piece speed are the most significant to influence surface roughness, followed by work speed. The optimum set of input parameters for minimizing the surface roughness has also been found.