Catenary is referred to as "the real mathematical and mechanical form" in the architectural field. Because of the unique phase control characteristic of the catenary, it has excellent ability in optical manipulation. Here, we propose an optical waveform conversion device based on optical fiber-integrated catenary ring-array metasurfaces. The device consists of a cascade structure of a single-mode fiber (SMF) and a graded-index fiber (GIF). At the GIF end, two kinds of catenary ring-array metasurfaces are introduced to realize beam shaping from Gaussian beam (GB) to Bessel beam. The device can selectively generate a focused or non-diffracting Bessel beam by changing the circular polarization state of the incident light. It is worth noting that under some parameters of the device, the output Bessel beam can break through the diffraction limit, which has potential applications in the fields of optical imaging, optical communication, and optical trapping.