Aiming at the problem of horizontal well hydraulic fracturing in formation with dip angle natural fractures, theoretical and experimental studies on the initiation and propagation of hydro-fracture from natural fracture are carried out. Simplifying the natural fracture as a transverse fracture perpendicular to the well axis, the method of calculating initiation pressure and stress intensity factor (SIF) are given, based on the theory of linear elastic fracture mechanics and the maximum stress criterion. Meanwhile, using a prefabricated transverse fracture to simulate natural fracture, laboratory hydraulic fracturing test is carried out to investigate the fracture geometry and initiation pressure. Theoretical calculation shows that: (1) after initiating from the prefabricated transverse fracture tip, the prefabricated transverse fracture and the fracture can be regarded as a whole and treated as a transverse fracture to calculate SIF when the fracture propagates longer than the radius of the notch tip. (2) when the distance between the fracture tip and the wellbore wall is longer than four times of the wellbore radius, the wellbore effect can be neglected and SIF equation for penny-shaped crack can approximately be used. Experimental studies show that (1) hydraulic fracture initiates at the tip of the prefabricated transverse fracture and propagates to form a transverse fracture orthogonal to the wellbore; fracture propagation shows the feature of model Ⅰ fracturing; the fracture geometry is near round; no longitudinal fracture is observed. (2) pumping rate has a significant effect on the net breakdown pressure and net initiation pressure with larger pumping rate leading to higher net pressures; the discreteness of net initiation pressure and calculated critical fracturing value KⅠ are small under both large and small pumping rate conditions. Research results can provide guidance for improving near wellbore fracture geometry of naturally fractured reservoir and reference for designing hydraulic fracturing with prefabricated transverse fracture in coal mining.