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Topological quantum materials have stimulated a growing attention because they reveal novel aspects of condensed matter physics and point to new opportunities in materials science, in particular for thermoelectrics. Here, we experimentally study thermoelectric effects in HfTe₅, which was predicted to be at the boundary between strong and weak topological insulators. The magnetic field dependence of HfTe₅ thermoelectric properties attests to the anomalous character of this material, supported by our angle-resolved photoemission spectroscopy (ARPES) measurements. A possible topologically non-trivial band structure is proposed to account for our observations. Our results constitute a highly constraining set of data for any model of transport based on HfTe₅ band structure. Furthermore, the extraordinary thermoelectric properties suggest a new paradigm for the development of thermoelectric applications based on layered transition-metal chalcogenides.