We report the fabrication and characterizations of oxide heterojunctions composed of TbMnO3 thin films grown on conducting Nb:SrTiO3 substrates. The heterojunctions exhibit rich rectifying characteristics, depending on not only the measurement temperature but also the growth temperature: at 300 K, good rectification appears in both samples; at lower temperatures, the rectification is much smaller in the sample grown at 700 °C, whereas it exhibits a reversed bias dependence and reaches ∼5000 in the sample grown at 780 °C. Regarding to the transport mechanism, the conduction appears to be Schottky-emission-like at high temperatures in both junctions, indicating well-defined band alignment at interface; on the other hand, the space-charge-limited mechanism dictates the low temperature transport. Furthermore, the temperature and frequency dependent capacitance-loss data suggest that the transport dynamics is associated with multiple thermally activated relaxation processes. Finally, transmission electron microscopy studies shed light on the crystalline quality of the junction interfaces, which is believed to dictate the corresponding transport properties