Flexible and transparent applications have become an emerging technology and have shifted to the forefront of materials science research in recent years. Transparent conductive oxide films have been applied for flat panel displays, solar cells, and transparent glass coatings. However, none of them can fulfill the requirements for advanced transparent flexible devices, such as high-frequency applications. Here, we present a promising technique for transparent flexible conducting oxide heteroepitaxial films: the direct fabrication of epitaxial molybdenum-doped indium oxide (IMO) thin films on a transparent flexible muscovite substrate. An n-type epitaxial IMO film is demonstrated with a mobility of 109 cm2 V−1 s−1, a figure of merit of 0.0976 Ω−1, a resistivity of 4.5 × 10−5 Ω cm and an average optical transmittance of 81.8% in the visible regime. This heteroepitaxial system not only exhibits excellent electrical and optical performance but also shows excellent mechanical durability. Our results illustrate that this is an outstanding way to fabricate transparent and flexible conducting elements for the evolution and expansion of next-generation smart devices.