The interlaminar fracture is the most common type of failure in polymeric textile composites because these composites are prone to delaminate under the influence of external loading. Depending on the type of deformation, the interlayer fracture can be Mode-I, Mode-II, Mode-III, and Mixed Mode-I/II type. In this research work, Mode-I interlaminar fracture modeling of carbon fiber reinforced polymer (CFRP) composite laminate is performed using a double cantilever beam (DCB) test specimen on ABAQUS software as a cost-effective numerical simulation approach. The finite element based fracture modeling techniques, virtual crack closure technique (VCCT), cohesive zone modeling (CZM), and extended finite element method (XFEM) were employed under the two-dimensional and three-dimensional interlayer crack propagation to evaluate the load-displacement responses. The interaction properties were applied between the top and bottom part of DCB specimen and the adhesive layer was modeled using the CZM approach. The numerically simulated responses were compared with the published experimental load-displacement responses and found to be in good agreement. All the fracture modeling approaches validate the experimental trend, however the three-dimensional XFEM technique was found to be the most suitable modeling approach for crack growth in adhesively bonded parts. The stress based criteria was used for crack initiation, whereas the energy based approach used for crack propagation in DCB laminate. The parametric study of various fracture parameters (cohesive strength, fracture energy, interfacial stiffness, laminate thickness, and pre-crack length) were also conducted to understand their effects on load-displacement responses of the Mode-I interlaminar fracture. The fracture modeling approaches were compared by considering the element type, shape, total elements, accuracy, run-time, increments, and convergence speed.