To model hydraulic fracture propagation in naturally fractured reservoirs, fracture propagation is generally assumed to be a single planar fracture propagated only in the vertical direction from a horizontal well, regardless of the presence of natural fractures. In this paper, we developed a multi-stage hydraulic fracture propagation model using a twisted multiple planar fracture that is able to describe the propagation of hydraulic fractures more realistically. In propagating hydraulic fractures, we used two criteria: maximum tangential stress, to determine the fracture initiation angle, and whether a hydraulic fracture passes through a natural fracture. The developed model was used with a commercial reservoir simulator through grid mapping in the form of a discrete fracture network using microseismic data. The results of the verification matched the experimental results well for various intersection angles and maximum horizontal stress directions. In the investigation of the direction of maximum horizontal stress, the frictional coefficient of the fracture interface, and fracture orientation, hydraulic fracture propagation modeling results showed that the hydraulic fracture passed through a natural fracture, and thereafter propagated in a manner suitably consistent with the theoretical results, based on a fracture interaction criterion. After confirming the twisted multiple planar fracture model suggested in this work, discrepancies were found in the fracture connectivity and the stimulated reservoir volume. This indicates that the twisted multiple planar fracture approach, which is more realistic in terms of fracture propagation, is extremely important in evaluating the initial gas in place, calculated according to the stimulated reservoir volume.