  Thermoelectric effects are more sensitive and promising probes to topological
properties of emergent materials, but much less addressed compared to other
physical properties. Zirconium pentatelluride (ZrTe$_{5}$) has inspired active
investigations recently because of its multiple topological nature. We study
the thermoelectric effects of ZrTe$_{5}$ in a magnetic field and find several
anomalous behaviors. The Nernst response has a steplike profile near zero field
when the charge carriers are electrons only, suggesting the anomalous Nernst
effect arising from a nontrivial profile of Berry curvature. Both the
thermopower and Nernst signal exhibit exotic peaks in the strong-field quantum
limit. At higher magnetic fields, the Nernst signal has a sign reversal at a
critical field where the thermopower approaches to zero. We propose that these
anomalous behaviors can be attributed to the Landau index inversion, which is
resulted from the competition of the $\sqrt{B}$ dependence of the Dirac-type
Landau bands and linear-$B$ dependence of the Zeeman energy ($B$ is the
magnetic field). Our understanding to the anomalous thermoelectric properties
in ZrTe$_{5}$ opens a new avenue for exploring Dirac physics in topological
materials.
