Natural fracture in shale formation is very developed. During fracking treatment, the natural fractures can be reactivated to form a complex network. In addition, the natural fracture is the medium for gas storage. Lots of gas exists in natural fractures in the form of free gas. Numerical simulation was used to study the interaction between hydraulic fracture(HF) and natural fracture(NF). The paper mainly focused on the reactivation and extension of NF caused by HF. The model includes three and single NF,respectively, and simulation variables corresponding to different angles of approach, differential stress and elastic parameters of formation. Results show that:(1)Formation breakdown stress is changing with corresponding angles of approach. When angle of approach is 90°,the water pressure for formation breakdown is the largest, and formation breakdown stress increase with increasing of differential stress. (2)Whether single or three natural fracture, after reinstating of natural fractures, the extension direction of branch fracture resume to the maximum horizontal principal stress. When angle of approach is 90°,the reactivated effect is best. (3)The branching HF presented double shift at tip of NF when angle of approach is 90°. It is helpful to form fracture network and large number of element burst in the model. The fracking effect is the best. (4)The critical water pressure for the reactivation of NF decrease with increasing of elastic modulus and deceasing of Poisson's ratio. The elastic properties of gas formation has a great influence on the formation of a fracture network. The fracking effect is good in formation with high elastic modulus and low Poisson's ratio.