Provided are an optical transmission line including a connected part of the optical fibers having different refractive index profiles, wherein at least one of the optical fibers has a hollow region, and a method for connecting such optical fibers, wherein connection loss in a connection of such optical fibers is reduced. In the case of connecting an optical fiber 1, which does not have a hollow region and which consists of a core region 3 and a cladding region 4, and an optical fiber 2, which consists of a hollow core region 5 and a cladding region 6 having a plurality of refractive index variation parts 7 which extend along optical fiber 2, matching oil M is first injected into the connecting end portion of the hollow core region 5 to be connected with the optical fiber 1. The matching oil M is a substance that has a matched refractive index greater than the refractive index of the material which forms the cladding region 6. Subsequently, one end portion of the optical fiber 1 and the connecting end portion of the optical fiber 2, wherein the matching oil M is injected, are inserted into the glass pipe 8, and the optical fiber 1 and the optical fiber 2 are connected.