The Airy beam in short-wavelength regime, endowed with tunable physical properties of self-acceleration, non-diffraction, and self-healing, holds significant promise for advancing high-resolution optical trapping and imaging. Here, we experimentally demonstrate a tunable blue-violet Airy beam generator based on non-degenerate four-wave mixing process in a diamond-type energy level system of Rb atoms. The 420 nm signal two-dimensional Airy beam is generated when the 780 nm Gaussian pump and the 776 nm probe Airy beams simultaneously interact with the atomic medium. The physical properties of the Airy beam are transferred from the near-infrared (776 nm) to the blue-violet (420 nm) wavelength via the non-degenerate four-wave mixing process. Compared to the input 776 nm probe Airy beam, the generated 420 nm Airy beam exhibits a ~ 1.86 times reduction in non-diffraction distance and a ~1.83 times increase in acceleration owing to the nonlinear frequency conversion. Additionally, the self-healing property of the generated 420 nm Airy beam is verified by the robust reappearance of the blocked beam main lobe. The all-optical control of the generated 420 nm Airy beam is achieved by tuning the Rb vapor temperature and the pump beam power, enabling dynamic manipulation of beam intensity and spatial profile. Our work establishes a versatile platform for generating tunable short-wavelength structured light field by nonlinear light-matter interactions, opening avenues for applications in optical information processing and precision microfabrication.