Hydraulic fracturing is known as the most important technical measure to enhance the reservoir recovery in tight formation, where the rock is fractured by the injection fluid to overcome the in-situ stress and rock tensile strength in 3D geological structure. How to accurately model such fluid-driven fracture propagation behavior is still challenging, especially considering the anisotropy of layered rock. We propose a novel 3D XFEM for fluid-driven fracturing of layered rocks, where the material properties and fracture toughness are anisotropic. The crack tip singular functions vary along the curved fracture front, which stems from differing crack tip asymptotes caused by variations in local material properties. These functions in three-dimensional anisotropic space are first established. A coordinate transformation is defined by the normal to curved fracture front at each quadrature point, and the global elastic stiffness matrix is transformed to calculate its local form. The characteristic equation, obtained by extracting the plane strain components from the local elastic stiffness matrix, is solved to compute the tip enrichment functions. Additionally, a hybrid explicit-implicit method is developed for fracture propagation and geometric description with rock anisotropy. In this approach, the explicit Irwin’s criterion is regularized by inverting the varying crack tip asymptotes at different fracture front nodes, which provides the anisotropic propagation distances and injection time constraint during each propagation step. The apparent Young’s modulus is introduced in the criterion to capture the variations of local material properties with propagation angle. The fracture surface is represented implicitly by level set functions, which are calculated from the fracture description updated through the Irwin’s criterion. This hybrid method avoids solving complex advection-type equations and improves the computational efficiency of nodal enrichment. The proposed method is validated against the analytical solution and various numerical cases with non-self-similar propagation behavior and strong fracture toughness anisotropy.