Radial wellbore fracturing technology is a new unconventional reservoir reconstruction technology, which is based on the radial wellbore drilled from the main wellbore. The influence of natural fracture on fracture initiation is studied after radial wellbore intersect with natural fracture. The analytical model of natural fracture activation by radial wellbore fracturing is established. The influence of natural fracture location, natural fracture dip angle, azimuth angle and reservoir in-situ stress state on fracture initiation is analyzed. The results show that: with the increase of the distance between the natural fracture and the main wellbore, the tensile activation pressure of the natural fracture increases significantly, while the shear activation pressure changes slightly.With the increase of the natural fracture dip angle, the natural fracture activation pressure increases, and the azimuth angle has no effect on the activation pressure.Under the normal fault and reverse fault stress state, the natural fracture is easy to activate; under the strike slip fault stress state, the natural fracture is difficult to activate. This study lays a foundation for the application of radial well fracturing technology in reservoirs with natural fractures.