In addition to artificial fractures generated by hydraulic fracturing technology, natural fractures distributed in reservoirs will also affect the fluid flow process. To study the transient behavior of the pressure in fluid flows in reservoirs containing natural fractures, a semi-analytical model for vertically fractured wells with complex natural fracture networks was established. This model was based on the linear source function theory and the fracture discretization and coupling methods. It was solved by the Stehfest numerical inversion and the matrix transformation. The results of the study on the fluid flow stages in a reservoir with natural fractures indicated that the presence of natural fractures increased natural fracture flows. These flows were dominated by natural fractures and fracture interference stages and were different from the fluid flows observed in vertically fractured wells with a single main fracture. The sensitivity analysis on the influences of the fluid flow factors in the reservoirs with three types of natural fractures could provide a more detailed reference for the identification of the reservoir parameters and the transient characteristics of the flow stage. The different characteristic curves of the fluid flow in the reservoirs with different scale natural fractures could also provide a theoretical basis for determining the distribution of natural fractures in reservoirs.