In precision turning, the quality of surface finish is an important requirement for machined workpiece. Thus, the choice of optimal cutting parameters is very important for controlling the required surface quality. The focus of the present study is to find a correlation between surface roughness and cutting parameters (feed rate, depth of cut) and nose radius in turning 3J33 maraging steel, and to derive mathematical models for the predicted surface roughness based on both of cutting parameters and nose radius. The experimental design is carried out using the quadratic rotary combination design. The regression analysis shows feed rate and nose radius influence surface roughness significantly. With F-ratio test the proposed model is adequate. The method could be useful in predicting roughness parameters as a function of cutting parameters and nose radius.