Abstract: The extension efficiency of multi-cluster hydraulic fractures is key to the fracturing effect of shale gas horizontal wells. Field monitoring has found that many perforating clusters fail to feed fluid, and issues with non-uniform initiation and propagation of multi-cluster fractures are prominent. It is crucial to deeply understand the influence of the natural fractures' spatial distribution on the competitive expansion of multi-cluster hydraulic fractures. Therefore, a three-dimensional fully coupled numerical model for three-cluster fracturing in randomly fractured shale reservoirs is established based on the discrete lattice method. This model accurately describes the entire process and evolution of multi-cluster hydraulic fracture competition, propagation, and interaction with natural fractures. The study investigates the behavior of multi-cluster hydraulic fracture propagation under the influence of in-situ stress differences, cluster spacing, fracturing fluid viscosity, and injection rate. Construction measures to enhance the efficiency of multi-cluster extension are proposed. The results indicate that when hydraulic fractures encounter natural fractures, they exhibit single or multiple composite modes such as penetration, turning, and bifurcation. The natural fracture network intensifies the stress shadow effect during the competitive expansion of multiple fracture clusters, causing inhibited perforating clusters to easily turn or bifurcate along natural fractures and fuse with other perforating clusters, thereby reducing the fracture extension scale. The smaller the stress difference and cluster spacing, the more pronounced the stress interference between fractures and the smaller the fracture extension scale. Increasing fracturing fluid viscosity or injection rate reduces the degree of stress disturbance of intermediate cluster hydraulic fractures, resulting in longer extension distances. It is recommended to increase fracturing fluid viscosity appropriately during the pre-fluid stage and displacement during the main fracturing stage to improve the extension efficiency of multi-cluster hydraulic fractures. The research findings can guide the segmentation of shale gas reservoir perforations and the optimization of fracturing parameters.