Flexible integrated circuits (ICs) have gained a lot of attentions in recent years for their emerging application in wearable electronics. Flexible thin-film transistors (TFTs) with low-cost and high-performance are highly desirable as essential and fundamental element for most of the flexible applications. In this paper, we fabricated single-crystalline silicon nanomembrane (SiNM) based TFTs with anodized aluminum oxide (AAO) as dielectric material on glass and flexible plastic substrates. Good quality AAO was obtained on plastic substrates at room temperature. AFM was used for surface morphology of AAO gate dielectric layers on different substrates (i.e. glass, polyethylene terephthalate (PET) and SU-8 coated PET). The electrical characteristics of the AAO gate dielectric layers on different substrates were also analyzed with metal- dielectric-metal (MIM) capacitors. SiNMs were processed with complementary metal oxide semiconductor (CMOS) compatible semiconductor process (e.g. photolithography, ion implantation, thermal annealing, reactive ion etching, metal evaporation, etc.), and then transferred to the substrates with AAO/aluminum stack layers. Performances of transistors on glass and plastic substrates were characterized. Compared with the TFT fabricated on glass substrate, TFT fabricated directly on a PET substrate have lower performance due to poor surface roughness. For optimization of the surface roughness, PET was modified with coating SU-8 photoresist. By this way, TFT had properties close to that on glass substrate. AAO that can be manufactured at room temperature provides a simple and low-cost solution for high-performance flexible single-crystalline SiNM TFTs.