Abstract Optical vortices usually carry integer orbital angular momentum (OAM) of light. Recently, optical vortices with rational-order OAMs have also been created continuously for entangling the super-position OAM states of monochromatic light in a single device. Here, we report the broadband generation of such rational-order optical vortex beams by using a bilateral meta-grating. The meta-grating contains two oblique gratings that encode two sign-opposite linear phase profiles in two symmetric sides, thus leading to phase dislocation along the symmetric axis. We reveal that the encoded phase profiles are valid in a range of wavelengths due to the broadband response of the meta-grating. The measured phase, intensity and tilting angles match perfectly with theoretical prediction, suggesting the bilateral meta-grating as a powerful device to create broadband and continuous OAM of light for various applications such as optical micro-manipulation, optical communication, quantum physics, and super-resolution imaging.