A series of finite-element analyses for slab–column edge connections reinforced with fiber-reinforced polymer (FRP) reinforcement and subjected to reversed-cyclic lateral load is conducted and discussed. A three-dimensional nonlinear finite-element model (FEM) is constructed using a commercially available software. The FEM is validated against the results of experimental studies conducted previously by the authors. Subsequently, the validated FEM is used to carry out an extensive parametric study investigating the influence of key parameters including the gravity shear ratio (0.2–0.8), flexural reinforcement type [glass and carbon FRP (GFRP and CFRP, respectively)], column aspect ratio (0.25–4.00), flexural reinforcement ratio (0.7%–1.4%), and slab thickness (150–400 mm). The results showed that the drift capacity of edge connections reinforced with either GFRP or CFRP reinforcement is reduced when the applied gravity shear ratio increases. However, GFRP-reinforced concrete (RC) connections were able to undergo larger drift ratios than their CFRP-RC counterparts. In addition, increasing the slab thickness reduced the punching shear strength of GFRP-RC connections, even for slabs with an effective depth less than 300 mm.