Hydraulic fracturing has been used as an indispensable method of improving energy productivity in oil, gas and geothermal reservoirs. Current experience of hot dry rock reservoir fracturing shows that new cracks are hard to create in intact hard rocks, and therefore, hydraulic fracturing in rock mass with pre-cracks is more efficient. However, there is a lack of easily applicable theoretical methods to predict the propagation direction of pre-cracks during hydraulic fracturing. In this study, a new method based on the hyperbolic failure envelope is proposed to qualitatively predict the crack-initiation direction of pre-cracks and to evaluate the failure mode of the rock adjacent to the crack tips during hydraulic fracturing. Results show that the failure mode of the rock and the crack-initiation direction at the pre-crack tips are dominated by the initial in-situ stress state and the mechanical properties of the rock. Four scenarios involving different crack-initiation directions and rock failure modes are discussed in this study, and corresponding crack propagation direction and failure mode are given. Numerical modeling results based on the extended finite element method show good agreement with theoretical prediction results. Comparisons with an experimental study from literature further verify the theoretical prediction and numerical modeling results. The proposed method can provide guidance for the hydraulic fracturing stimulation of not only geothermal energy reservoir, but also oil and gas reservoirs with pre-existing natural fractures.