With the development of DC power supply systems, breaking capacity of circuit breakers has been increasingly unable to meet the growing requirements for DC system short-circuit current level. To ensure the safety of the systems, a fault current limiter must be used in series with circuit breakers. The properties of superconducting fault current limiters such as fast reaction rate, simple structure, small size have caused widespread concern, the research on superconducting fault current limiters is becoming a hotspot in the field of DC system protection. In the paper, the FEM computational models of superconducting fault current limiters for the steady-state operation and the transient impulse are established. Using the steady-state model, we have calculated the magnetic field distribution and the inductance of superconducting coils, and using the transient impulse model, we have analyzed the transient magnetic field distribution of superconducting coils and electromagnetic force on the coils. On the basis of the calculation of the magnetic field, the influences of magnetic field distribution on the critical current at the steady-state and the current limit characteristics at the transient impulse of the superconducting coils with different structures and geometries are studied. The results can be used for performance analysis and design optimization of superconducting current limiters. In addition, an experimental model of superconducting current limiters, which is used to verify field calculation results, is developed, and the relevant data is measured.