Tight reservoirs, as an important alternative for conventional energy resources, have been successfully exploited with the aid of hydraulic fracturing technologies. Because of the inherent ultralow permeability and porosity, tight oil reservoirs generally suffer from the effects of stress sensitivity. Both hydraulic fractures with complex geometries and a high-permeability area known as stimulated reservoir volume (SRV) may be generated by the massive hydraulic fracturing operations. All these bring huge challenges in transient pressure analysis of tight reservoirs. Up till now, although many research studies have been carried out on the transient pressure analysis of volume-fractured horizontal wells in tight reservoirs, unfortunately, there is still a lack of research studies that have taken stress sensitivity, complex fracture networks, and the SRV into consideration, simultaneously. To fill up this gap, this paper first idealizes the reservoir after hydraulic fracturing as two radial composite regions, that is, the unstimulated outer region and the inner SRV. The stress sensitivity is characterized by the variable permeability depending on the pore pressure. A linear source with consideration of the stress sensitivity in the composite reservoir is obtained by the perturbation technique, Laplace transformation, and the flow coupling of two regions. Second, the complex fracture networks are discretized into segments to capture their geometries. A semi-analytical model is finally established and validated by the comparison with previous models. On the basis of our model, six flow stages of volume-fractured horizontal well are identified and special features of each regime are analyzed. The stress sensitivity has a great impact on the later stage of production. The mobility ratio and the SRV radius mainly affect SRV pseudo-steady-state flow period and interporosity flow period in the outer region. Fracture number mainly affects the linear flow in the SRV. Fracture geometries mainly affect linear flow and interporosity flow in the SRV. This study has some significance for well test interpretation and production performance analysis of tight reservoirs.