Recently, hybrid beams spark considerable interest because of its properties coming from different kinds of beams at the same time. Here, we experimentally demonstrated Airy vortex beam generation in nonlinear frequency conversion process when the fundamental wave with phase modulated by a spatial light modulator 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 beam which may broaden its future use in optical manipulation and light-sheet microscopy.