Recently, hybrid beams have sparked considerable interest because of their properties coming from different kinds of beams at the same time. Here, we experimentally demonstrate Airy vortex beam generation in the nonlinear frequency conversion process when the fundamental wave with its phase modulated by a spatial light modulator is incident into a homogeneous nonlinear medium. In our experiments, second harmonic Airy circle vortex beams and Airy ellipse vortex beams were generated and the topological charge was also measured. The parabolic trajectory of those Airy vortex beams can be easily adjusted by altering the fundamental wave phase. This study provides a simple way to generate second harmonic Airy vortex beams, which may broaden its future use in optical manipulation and light-sheet microscopy.