Current-limiting superconducting cable uses the quench resistance of superconductor under short-circuit current to improve the short-circuit impedance of the system. In this paper, the design of current-limiting 10 kV three-phase tri-axial superconducting cable is studied. The design methods of cable conductor layer, insulation layer and current-limiting characteristics are given, and one 5 m-long sample is fabricated for testing. The sample is made of stainless-steel-reinforced yttrium barium copper oxide (YBCO) tape, with an expected rated current of 2.5 kA and rated voltage of 10 kV. The test results show that the designed cable can transmit a maximum AC current of 3.0 kA at 77 K. The cable has passed the power frequency withstand voltage, partial discharge and lightning impulse tests. The current limiting characteristics under the action of DC pulse current show that the cable can quickly quench and produce resistance, and the corresponding equivalent resistance value also changes along with current amplitude and duration.