Thermoelectric (TE) materials, with the ability to convert heat directly to electricity, have attracted worldwide increasing attention due to the strong urge for clean energy today. However conventional TE devices suffer from the low conversion efficiency for decades due to the trade-off between TE parameters. Novel quantum materials such as topological insulators with unique boundary states protected topologically against backscattering offer a new way for designing high-performance TE devices. Here we demonstrate that topological insulator nanoribbons, which exhibit unconventional TE behaviors, can greatly improve the TE efficiency. As an example, we calculate the TE properties of the ZrTe5 nanoribbon through the Boltzmann transport theory with the electronic bands and the thermal conductivity obtained from ab initio calculations. The dramatic difference in the scattering intensity between the in-gap topological edge states and the bulk states originates several unusual TE behaviors: (I) The electrical to electronic thermal conductivity ratio can be several times larger than that predicted by the Wiedemann-Franz law. (II) The reduced Seebeck coefficient shows an anomalous opposite sign to that of normal semiconductors with the magnitude much larger than unity. (III) By properly introducing defects, the thermal conductivity can be significantly reduced without noticeably deteriorating the electrical conductivity. (IV) Under appropriate strain, the electrical to electronic thermal conductivity ratio could be tens of times larger due to the bulk gap narrowing. These results indicate that a figure of merit larger than ten is highly likely.