Large-diameter gas extraction borehole is considered an effective method by which to realize coal mine methane exploitation and outburst prevention. Efficient gas extraction can be achieved by selecting the right borehole parameters. In this paper, by comparing several conventional objective weighting methods, the PCA was used to assign the weights to the research indices, the optimization objective was reduced from multi-dimensional to one-dimensional with the help of the gray correlation analysis. The study of gas extraction effect under different borehole parameters based on the response surface model. Numerical simulations were used to analyze the mixed volume of gas extraction, the pure volume of extraction and the concentration in the upper corner after extraction under different schemes. Finally, a genetic algorithm degree model was used to solve the solution and determine the optimal arrangement of borehole parameters. The study shows that (1) the weight shares of borehole stratum, borehole diameter and borehole spacing were 0.385, 0.285 and 0.33, respectively, in the reduced dimensional analysis of the PCA. (2) Using the results of improved gray correlation analysis as a comprehensive evaluation value to measure the effect of gas extraction, the optimal range of the model was 28–30 m borehole level, 190–210 mm borehole diameter and 5.5–6.5 m borehole spacing. (3) Using the genetic algorithm to solve the model, we obtained the borehole layer 28.79 m, borehole diameter 199.89 mm, borehole spacing 5.76 m. The borehole gas extraction effect was good under this parameter. The extraction mixed volume was 129.8 m³/min, the extraction pure volume was 9.16 m³/min, the upper corner concentration was 0.52%, and the prediction accuracy of the model was 97.8%.