In naturally fractured shale oil and gas reservoirs, it is expected that the hydraulic fracture behavior is significantly influenced by the interaction with pre-existing natural fractures. However, the relationship between fracture behaviors and natural fractures has not been sufficiently clarified because direct observation of all the fractures or microcracks generated during the field or laboratory scale hydraulic fracturing is difficult. In this paper, a series of flow-coupled DEM simulations varying the properties of natural fracture, such as the permeability of natural fractures and the angle between created hydraulic fracture and natural fracture (approach angle), is presented. As a results, different fracture growth patterns were observed with different combination of approach angle and permeability of natural fracture. When the approach angle is high and the permeability is low, the hydraulic fracture ignores the existence of natural fracture and it propagated straight to the direction of maximum compressive principal stress. On the other hand, when the approach angle is low and the permeability is high, hydraulic fracture propagated along with a natural fracture. After that, it branched or curved to the direction of maximum principal stress.