Shape memory fibrous membranes (SMFMs) are an emerging class of active polymers, which are capable of switching from a temporary shape to their permanent shape upon appropriate stimulation. Quintuple-shape memory membranes based on the thermoplastic polymer Nafion, with a stable fibrous structure, are achieved via electrospinning technology, and possess a broad transition temperature. The recovery of multiple temporary shapes of electrospun membranes can be triggered by heat in a single triple-, quadruple-, quintuple-shape memory cycle, respectively. The fiber morphology and nanometer size provide unprecedented design flexibility for the adjustable morphing effect. SMFMs enable complex deformations at need, having a wide potential application field including smart textiles, artificial intelligence robots, bio-medical engineering, aerospace technologies, etc in the future.