Hydraulic fracturing is the core technology of shale gas reservoir exploitation. In the process of fracturing, the expansion of hydraulic fractures will encounter natural fractures. After intersecting with natural fractures, the expansion characteristics of fractures have a significant impact on the formation of fracture network, thus affecting the final fracturing reconstruction effect. Based on cohesion unit, a seepage-stress-fracture coupling model of hydraulic fractures intersecting with multiple natural fractures in shale gas reservoir was established based on fracture mechanics. The propagation patterns of hydraulic fractures and natural fractures under different natural fracture inclination, natural fracture size, stress difference, fracturing fluid displacement and viscosity were studied. The fracture morphology classifier based on Bagging algorithm integrated support vector machine (SVM), decision tree classifier (DTC), logistic regression (LR) and k-nearest neighbor algorithm (KNN) was used to predict the fracture intersection propagation morphology, and the prediction results of Bagging algorithm were compared with those of SVM, DTC, LR and KNN algorithms. The results show that the prediction accuracy of the intersection propagation morphology of hydraulic and natural fractures based on Bagging integrated algorithm reaches 92.58%, and the maximum improvement is 17.95% compared with a single algorithm. The smaller the stress difference, the larger the natural fracture inclination, the larger the fracture size, and the lower the fracturing fluid displacement and viscosity, the more easily shear fractures are generated. Otherwise, the more easily perforated fractures are formed. The path and shape of fracture propagation are intelligently predicted through the established data set of hydraulic fracturing prediction results, which provides a method reference for the optimization design of well completion fracturing by using artificial intelligence and machine learning algorithms and an important reference for the optimization design of actual fracturing process.