<p>Low-velocity pre-Darcy is generally found in low-permeability reservoirs. This study utilizes a fully implicit nonlinear solver based on Newton iteration to simulate fluid flow of the vertically fractured well in low-permeability reservoirs, and the computational framework systematically integrates the pre-Darcy flow, fracture topology, embedded discrete fracture model, and stress sensitivity. To ensure the algorithm's accuracy, the proposed numerical solution is validated by using the numerical simulator. Based on the numerical solution proposed in this work, six typical flow patterns may be observed from the pressure fields with different production times. Meanwhile, the simulation results indicate that pre-Darcy flow characterized by the pseudo-threshold pressure gradient is not only unbeneficial to the well’s high production but also greatly impacts the seepage area of the vertically fractured well. Moreover, a larger stress sensitivity modulus in hydraulic fracture or natural fracture will lead to lower production of the vertically fractured well due to its effect on fracture permeability. In addition, tree topology is conducive to obtaining the highest cumulative oil production during the late flow period.</p>