La0.6Sr0.4Co0.2Fe0.8O3−δ (LSCF) hollow fiber membranes are usually fabricated through slurry spinning process followed by one-step sintering. While high oxygen permeation performance can be obtained, the designs lack sufficient mechanical strength, limiting further upscaling for stack and module development. This research studies a functionally graded hollow fiber LSCF membrane with a three-layer structure, i.e., thick LSCF-ZnO substrate/dense thin film LSCF/porous, thin LSCF catalyst layer. The thick substrate provides sufficient mechanical strength to support the membrane while facilitating facile gas diffusion with embedded open microchannels. The dense thin film LSCF separation layer decreases bulk diffusion resistance. The porous thin LSCF catalyst layer increases the reaction area for surface exchange process. The synergetic combination of the three layers enables to improve both mechanical strength and permeation performance. A stack with three parallelly-connected hollow fibers is assembled to demonstrate its potential capability for upscaling. Permeation performance is systematically measured and accelerated long-term stability is conducted for both the single membrane and the stack. The single membrane and the stack obtain oxygen permeation flux of ∼1.9 and 1.1 ml⋅cm−2⋅min−1 at 900 °C, respectively, and demonstrate excellent stability and robustness during a long-term test of ∼400 h and ∼20 thermal cycles between 600 and 900 °C. Membrane samples are characterized before and after the test. Experimental data are analyzed, and fundamental mechanisms are discussed.