The metasurface has recently emerged as a powerful platform to engineer wave packets of free electron radiation at the mesoscale. Here, we propose that Airy beams can be generated when moving electrons interact with bianisotropic metasurfaces. By changing the intrinsic coupling strength, full amplitude coverage and 0-to-π phase switching of Smith-Purcell radiation can be realized from the meta-atoms. This unusual property shifts the wave front of the assembled Airy beam toward a parabolic trajectory. Experimental implementation displays that evanescent fields bounded at slotted waveguides can be coupled into Airy beams via Smith-Purcell radiation from a designed bianisotropic metasurface. Our method and design strategy offer an alternative route toward free-electron lasers with diffraction-free, self-accelerating, and self-healing beam properties.