Extensive studies of electron transport in Dirac materials have shown positive magnetoresistance (MR) and positive magnetothermopower (MTP) in a magnetic field perpendicular to the excitation current or thermal gradient. In contrast, measurements of electron transport often show a negative longitudinal MR and negative MTP for a magnetic field oriented along the excitation current or thermal gradient; this is attributed to the chiral anomaly in Dirac materials. Here, we report a very different magnetothermoelectric transport behavior in the massive Dirac material ZrTe5. Although thin flakes show a commonly observed positive MR in a perpendicular magnetic field, distinct from other Dirac materials, we observe a sharp negative MTP. In a parallel magnetic field, we still observe a negative longitudinal MR, however, a remarkable positive MTP is observed for the fields parallel to the thermal gradients. Our theoretical calculations suggest that this anomalous magnetothermoelectric behavior can be attributed to the screened Coulomb scattering. This work demonstrates the significance of impurity scattering in the electron transport of topological materials and provides deep insight into the magnetotransport phenomena in Dirac materials.