Different from the fault current limiters used for an AC transmission system or a bipolar DC transmission system, a fault current limiting device for a multi-terminal flexible DC system should be able to effectively curb the rapid rise of fault current to avoid the lock of the bridge arm of current converter before the action of the line breaker. To satisfy this requirement, a basic structure and working principle of a new type of superconducting fault current limiter for a multi-terminal flexible DC power grid are proposed and a lab prototype for proof-of-principle is built. Through a series of experiments carried out on the prototype, the feasibility of the working principle and the designed structure has been confirmed. The test results have adequately demonstrated the functional characteristics of this kind of fault current limiter, such as that the current limiter can make full use of the maximum permeability of the iron core to achieve the maximum inductive impedance, and suppress the rising rate of the fault current within a few milliseconds after a short-circuit fault takes place. In addition, the current limiting threshold of the current limiter can be set by adjusting the number of superconducting isolation rings, so it can be flexibly adapted to different DC systems. This work is supported by the National Natural Science Foundation of China (No. 51677131).