This paper presents a new approach for the low voltage ride-through capability enhancement of doubly-fed induction generator (DFIG) wind farms using a hybrid superconducting fault current limiter (SFCL) of the first peak current limiting type, which has the advantage of a fast recovery time. A design for the hybrid SFCL, focusing on current limiting reactor (CLR) reactance calculation, is proposed in this paper to determine an appropriate value for the CLR reactance that satisfies the grid code requirements of the DFIG wind turbines. High-temperature superconductors (HTS) such as Bi-2212, YBCO, Bi-2223, Ti-2223, and Hg-1223 are investigated for use in the hybrid SFCL. The recovery time and first peak current reduction effectiveness are the criteria for selecting the HTS. In the proposed method, a during-fault voltage from the grid code requirement is used as an input parameter to compute the reactance of the CLR.Based on the results of the base-case simulations conducted on the DIgSILENT PowerFactory software, the Bi-2223 HTS with the first peak of fault current less than 4.5 kA and recovery time of 2.5 s is selected for adoption in the hybrid SFCL. The calculated results of the proposed method are compared with the simulation results of the hybrid SFCL, in terms of the DFIG wind turbine fault ride-through capability enhancement, to demonstrate that the performance of the proposed method satisfies the grid code requirements.