Orthorhombic HoMnO3 films with c-axis and a-axis orientations were prepared epitaxially on Nb-1.0 wt %-doped SrTiO3 single crystal substrates by using pulsed laser deposition technique to fabricate all-oxide heterojunctions. The temperature dependent current-voltage measurements display diodelike rectifying behaviors, and the forward current was perfectly fitted using the thermionic emission model. An anomalous increase in the reverse-bias current with decreasing temperature was observed in c-axis-oriented HoMnO3/Nb-doped SrTiO3 junctions, which was not found in a-axis-oriented ones. The tunneling through the junction, which depends on the effective barrier height at the interface, was used to explain the results.