Abstract: The fracture-network fracturing or staged fracturing reformation technology for unconventional and tight reservoirs focuses on the scientific problem about the staggered extension of hydraulic fracture and natural fracture. To better control the extension azimuth of hydraulic fracture and achieve the optimal fracture network state, a two-dimensional fracture extension calculation model was built based on displacement discontinuity and element superposition principle, so as to conduct the quantitative simulation research on the staggered extension laws of a hydraulic fracture and a natural fracture under the conditions of different dip angles, intervals and stresses. The research results show that fracture intervals and dip angles can greatly affect the fracture extension amplitude. When the interval between natural fracture and fracturing fissure is greater than 1 m and the dip angle is less than 70°, the fracturing fissure will force the natural fracture to turn and extend until intersection. Principal stress ratio has an effect on the extension amplitude of staggered fracture to some extent. However, the Poisson's ratio and Young's modulus have insignificant influences on the extension amplitude of staggered fractures.