A superconducting cable includes a first conductor layer formed of superconducting wires, and an insulating layer formed at the outer periphery of the first conductor layer. The first conductor layer is an assembly of a plurality of superconducting wires obtained by forming an RE based superconductor layer on a metal substrate. The current is limited by an electrical resistance generated when the current of the first conductor layer exceeds the critical current, thereby preventing the superconducting cable from being damaged. A superconducting cable line is formed of a base and a current limiter, which is formed by using the above-described superconducting cable. Accordingly, when a current exceeding the rated current of the base flows, it can be damped.