The　performance　of　optical　fiber　communication,　laser,　and　sensing　systems　is　ultimately　limited　by　the　attenuation　of　optical　fiber,　which　cannot　be　lower　than　the　barrier　set　by　Rayleigh　scattering　in　bulk　silica　glass.　In　this　work,　the　longstanding　Rayleigh　scattering　limit　is　conquered　by　using　a　hollow-core　fiber　(HCF).　Two　visible-guiding　hollow-core　conjoined-tube　anti-resonant　fibers　are　successfully　fabricated　and　exhibit　overall　losses　of　3.8　dB　km(-1)　at　680　nm　and　4.9　dB　km(-1)　at　558　nm,　respectively.　The　latter　surpasses　the　Rayleigh　scattering　limit　of　silica　glass　fiber　by　2　dB　km(-1)　at　the　corresponding　wavelength.　Numerical　simulations　indicate　that　the　loss　level　the　authors　achieve　is　still　much　higher　than　the　ultimate　loss　limit　caused　by　surface　scattering　of　this　HCF　geometry,　leaving　plenty　of　room　for　further　refinement.