In the resistance spot welding (RSW) process of body structures, the initial gap (IG) occurs frequently. The RSW with IG impact welding quality, and subsequently reducing the structural safety of the whole vehicle. An equivalent displacement method (EDM) is proposed, and a refined finite element model (FEM) is established to accurately simulate the mechanical responses of the RSW with IG under tensile shear loading. This research chose 3 IGs (0 mm, 3 mm and 5 mm) of RSW for investigation. First, a true stress-strain curve of base metal (BM) is obtained by uniaxial tensile test, and hardness of the 3 zone is obtained through hardness test. Then, the stress-strain curves of heat-affected zone (HAZ) and fusion zone (FZ) are fitted from those of BM based on relationship between Vickers hardness and tensile strength. Then, the refined 3D FEM of RSW with initial gaps are established based on EDM. Finally, the model is nonlinear analyzed and compared with the experiment. The results show that the force and displacement curves obtained through simulation are highly consistent with the ones obtained through experiments with the maximum mean integrated relative error (MIRE) is 7.42 %. The average error of the maximum load-bearing capacity is 1.05 %, and the maximum error is 2.58 %. The failure modes are both button pullout, attributed to the relatively low strength of BM. And cracks occur in BM near HAZ and penetrate along the sheet thickness direction. These findings show that numerical simulation of RSW with IG, based on the EDM, effectively reflects its mechanical properties and failure behaviors.