Summary The shape, size, and orientation of natural fractures significantly impact the geometry of hydraulic fractures in unconventional reservoirs, such as shale gas/oil, tight gas, and enhanced geothermal system. The behaviors after the hydraulic fracture encounters natural fractures have been summarized as crossing, diverting, step over, and stopping based on a great number of numerical and experimental analysis with plain strain assumptions. However, under practical situations, the geometries of natural and hydraulic fractures are much more complex than the vertical and rectangular shape assumed by 2D models. The experimental studies on the role of height and inclination of natural fractures have revealed some other phenomena (e.g., bypassing process that the fluid-driven hydraulic fracture propagates up the back side of the natural fracture), which are unable to be captured in 2D. To better describe the intersection behaviors among different kind of fractures, a fully 3D model based on the displacement discontinuity method (DDM) is developed on top of our previous models, which only considered the propagation of hydraulic fractures. A novel crossing criterion to judge whether the hydraulic fracture will cross the cemented natural fracture in 3D is proposed. The successive node snapping scheme is adopted to construct conforming meshes for the evolving intersected curves between hydraulic and natural fracture surfaces, which only alters the location of a small fraction of nodes without changing the nodal connectivity. With this model, the evolution of fracture geometry after the hydraulic fracture intersects with the natural fractures of different toughness, size, orientation, and number is investigated. Because an extra dimension is considered, the fractures are allowed to propagate in more directions, resulting in a series of complex fracture geometries. The dynamic grid evolution method proposed in this work can promote the development of DDM in modeling fully 3D fracture networks in naturally fractured reservoirs.