Tight gas development has greatly contributed to the world’s energy supply. Pressure transient analysis (PTA) has extremely helped the development of tight gas. In this paper, a three-dimensional numerical model for transient pressure analysis of multi-stage fractured horizontal wells (MFHWs) in tight gas reservoirs was proposed, which was based on the embedded discrete fracture model (EDFM). Stress sensitivity of tight reservoir, and high-velocity non-Darcy flow in fractures were considered in this model, and the model was solved by Matlab Reservoir Simulation Tool (MRST). The discrete process of governing equations is described in detail, the typical MFHW pressure transient response curve of a tight gas reservoir was obtained, different flow regimes were divided, and three-dimensional pressure distribution profile of different flow stages were drawn to clearly understand the flow states of tight gas in the reservoir. The effects of different flow mechanisms and fracture properties on the log–log curves of the MFHW pressure transient response were analyzed in detail. The numerical PTA model proposed in this paper not only considers a variety of complex flow mechanisms of tight gas, but also accurately describes the characteristics of complex fracture network of tight reservoirs in three-dimensional conditions through EDFM. In addition, the problems of the incomplete description of tight gas flow stages by conventional analytical methods and semi-analytical methods were avoided through the numerical solution. The pressure response behavior of fluid in tight gas reservoir can be better explained by using this model, which helps to reduce the uncertainty of tight reservoir development.