Optical vortex is normally generated via a beam shaping process by irradiating a Gaussian beam through an external optical element or structure. Laser induced photorefractive structures can direct endow beam shaping functions inside materials， which can be stable and easy for the integration of devices. However， this is a method based on linear diffraction and normally cannot obtain efficient second harmonic optical vortex. To solve this problem， firstly， the effects of laser writing parameters on the resolution and maximal depth of photorefractive structures were experimentally investigated in lithium niobite. As a proof of concept， cross-shaped second harmonic vortex beams were obtained by illuminating a fundamental Gaussian beam through a 3D fork hologram. Then it was theoretically demonstrated that phase-matched second harmonic vortex beams can be generated by utilizing the Bragg diffraction of fundamental beam in the wavelength range between 1.074~3.716 μm.