A substrate having a transparent electrode for a flexible display which has flexibility and transparency and is resistant to stress of bending, and a method of fabricating the same are provided. By forming a transparent electrode of nanowires resistant to stress of bending on a substrate formed of a shape memory polymer (SMP) material, an increase in resistance due to bending can be prevented and the original form can be recovered. The method for fabricating a substrate having a transparent electrode for a flexible display includes: applying a nanowire dispersion solution of methanol to a glass substrate to form a nanowire electrode; coating the glass substrate with the nanowire electrode formed thereon, with an acrylic shape memory polymer (SMP) to form an SMP thin film; curing the SMP thin film through UV irradiation to form an SMP substrate; and removing the glass substrate from the SMP substrate.