Abstract: Multi-cluster staged fracturing technology of horizontal well is the core technology to develop shale gas reservoirs. In order to improve horizontal-well fracturing effect, therefore, it is of great significance to analyze the synchronous propagation laws of multiple fractures in the horizontal section and optimally design the cluster spacing in the horizontal section. In this paper, the mathematical model for the synchronous propagation of multi-cluster fractures was established based on the concept of dynamic flow rate distribution of multi-layer fracturing. In this model, the effects of stress interference between fractures, perforation, frictional pressure drop loss and filtration are taken into account. It was solved by means of the modified Picard method and then sensitivity analysis was conducted. It is shown that the effect of cluster spacing on multi-cluster fracture propagation is the most obvious, and when the cluster spacing is up to the fracture height, the stress interference between fractures is almost negligible. The shorter the cluster spacing, the more obvious the stress interference on the whole fracture cluster system. The fracture width can be improved significantly by increasing the viscosity of fracturing fluid, and in a way the effect of stress interference can be offset. The stimulated reservoir volume will be decreased significantly as the formation filtration coefficient increases, and the effect of perforation density on fracture cluster propagation is less. Finally, based on the proposed numerical model for the multi-fracture propagation in horizontal section, the mathematical model establishment procedure was simplified. It not only considers comprehensively the rock mechanics and engineering factors that have effect on fracture propagation, but also does the calculation fast, accurately and reliably. It provides the technical support for the design optimization of cluster spacing in horizontal sections.