The fracture network of the Y214 block in the Changning area of China is complex, and there are significant differences in the productivity of different shale gas wells. However, traditional machine learning models have problems such as missing key parameters, poor fitting effects and low prediction accuracy, which make it difficult to effectively evaluate the impact of crack network complexity on productivity. Therefore, the Pearson correlation coefficient was used to analyze the correlation between evaluation parameters, such as mineral content, horizontal stress difference, natural fractures and gas production. Combined with the improved particle swarm optimization (IPSO) algorithm and support vector machine (SVM) algorithm, a fracture network index (FNI) model was proposed to effectively evaluate the complexity of fracture networks, and the model was verified by comparing it with the performance evaluation results from the other two traditional models. Finally, the correlation between the fracture network index and the actual average daily gas production of different fracturing sections was calculated and analyzed. The results showed that the density of natural fractures was the key factor in controlling gas production (the Pearson correlation coefficient was 0.39), and the correlation between other factors was weak. In the process of fitting the actual data, the coefficient of determination, R², of the IPSO-SVM-FNI model training set increased by 8% and 24% compared with the two traditional models, and the fitting effect was greatly improved. In the prediction process based on actual data, the R² of the IPSO-SVM-FNI model test set was improved by 22% and 20% compared with the two traditional models, and the prediction accuracy was also significantly improved. The fracture index was concentrated, and its main distribution range was in the range of [0.2, 0.8]. The fracturing section with a higher FNI showed higher average daily gas production, and there was a significant positive correlation between fracture network complexity and gas production. Indeed, the research results provide some ideas and references for the evaluation of fracturing effects in shale reservoirs.