Nano-clean fracturing fluids have broad application potential in coalbed methane reservoir fracturing owing to their high stability, good temperature resistance, low filtration loss, and strong frictional resistance reduction. However, the sand-carrying regularity of nano-clean fracturing fluids in coalbed methane reservoirs is unclear, especially for complex fractures with variable directions. This study established a sand transport model that considers proppant collision, wall friction blocking, fracture fluid filtration loss, and the fracture branching angle to study the sand-carrying law of nano-clean fracturing fluids and its influencing factors in complex fractures. The degrees of influence on equilibrium height and placement rate from high to low were the proppant particle size, proppant density, fracturing fluid properties, sand ratio, and pumping discharge volume, and the correlation degrees obtained by grey correlation analysis are 0.862, 0.861, 0.855, 0.854, and 0.832, respectively. As the complexity of the fractures deepens and the resistance increases, the flow rate of the fracturing fluid is reduced, making it difficult for the proppant to enter the branching joints. The sand-carrying performance of a nano-clean fracturing fluid is better than that of a common clear-water fracturing fluid. The fluid-structure coupling model of a nano-clean fracturing fluid can accurately characterize the sand-carrying law of nano-clean fracturing fluids, providing a research basis for optimizing high efficiency sand-carrying fracturing fluid parameters in coalbed methane reservoir fracturing construction.