Different from oil properties, gas properties (gas formation factor, viscosity, and Z-factor, etc.) have nonlinear behaviors with pressure changes. However, many scholars use the average pressure or pseudopressure concept to simplify the phenomenon for easier solutions. Gas flow in shales is believed to be a complex process with multiple flow mechanisms including continuum flow, slip flow, diffusion, ad-desorption, and the stress sensitivity of fractures (natural or induced) permeability in multiscaled systems of nano- to macroporosity. Multistage hydraulic fracturing not only creates the stimulated rock volume (SRV) to improve production but also makes the flow in shales more complex. In this work, a rectangular composite model for a multistage fractured horizontal well (MFHW) with finite conductivity in shale gas considering the multiple flow mechanisms and multi-nonlinearities is developed. Comparing with the existing models for MFHW in shale, the model presented here takes strong nonlinearity of gas properties, hydraulic fracture asymmetry, fracturing efficiency, and SRV region into account, which is more in line with field practice. Numerical simulation of fully implicit control volume finite element (CVFE) based on unstructured 3D tetrahedral mesh is proposed to obtain the production performance of MFHW. Sensitivity analysis focuses on the effects of nonlinearity, Langmuir volume, stress sensitivity, finite conductivity, and SRV type on the production performance. The research and the numerical results obtained in this work can provide theoretical guidance to efficient and scale development for shale gas reservoir.