Natural fractures in reservoirs have a significant influence on hydraulic fracturing propagation. However, existing analyses have neglected the effect of natural fracture deformation parameters, including crack normal stiffness and shear stiffness on hydraulic fracturing. Therefore, a fractured reservoir model is established using ABAQUS to consider the effect of crack deformation parameters on hydraulic fracturing. A program for inserting global cohesive elements is developed to overcome the limitation of the basic cohesive elements only propagating along the preset path. Further, the bilinear traction-separation constitutive model is used to describe crack initiation and propagation. The analysis focuses on the effect of in situ stress conditions, natural fracture strength parameters (e.g., crack bonding strength), natural fracture deformation parameters (e.g., crack normal and shear stiffness), fracturing-fluid injection rate, and fracturing-fluid viscosity on hydraulic fracturing propagation. The results reveal that the hydraulic fracture initiation pressure increases with the horizontal stress difference, crack bonding strength, injection rate, and fracturing-fluid viscosity but decreases with increasing crack normal and shear stiffness. Additionally, lowering the horizontal stress difference, crack bonding strength, normal and shear stiffness, and fracturing-fluid viscosity results in a more complex fracture network. The total hydraulic fracture length and area increase with the horizontal stress difference and injection rate but decrease with increasing bonding strength, normal and shear stiffness, and fracturing-fluid viscosity. A higher crack bonding strength, crack normal stiffness, shear stiffness, and fracturing-fluid viscosity can improve the hydraulic fracture width and reduce the risk of sand plugging.