Abstract: To investigate the propagation and evolution laws of induced cracks in rocks under directional hydraulic fracturing, a phase-field model was developed. A dimension-reduced interface phase field model was adopted to characterize prefabricated cracks in order to optimize the modeling process. The model’s effectiveness was verified by comparison with the hydraulic fracturing tests of sandstone. The model was used to study the effects of pre-crack inclination, fracturing fluid viscosity, fluid injection rate, horizontal stress difference, and natural fracture on the hydraulically induced fracture expansion path and rock fracture pressure. The results show that changing the inclination angle of the pre-crack will lead to different degrees of deflection of the hydraulic-induced crack propagation path. The larger the fracturing fluid viscosity or injection rate is, the larger the breakdown pressure is, but the change of hydraulic-induced fracture propagation deflection angle is not affected. With the increase of horizontal stress difference, the breakdown pressure and hydraulic-induced fracture deflection angle show linear decreasing and nonlinear increasing trends, respectively. The different approach angles at the intersection of hydraulically induced fractures and natural fractures lead to the penetration or extensional expansion mode. Generally, the hydraulically induced fractures tend to expand in the direction of the maximum horizontal principal stress.