Topological quantum materials have stimulated 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. At 36 K, the thermopower of -277 mu V/K ( is reached when a field of 0.4 Tesla is applied, while it is -157 mu V/K ( at zero field and a large Nernst coefficient up to 600 mu V/K ( is observed at 100 K with magnetic field of 4 T. A possible topologically nontrivial 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.