We present oxide bipolar heterojunction diodes consisting of p-type ZnCo2O4 and n-type ZnO fabricated by pulsed-laser deposition. Hole conduction of ZnCo2O4 (ZCO) was evaluated by Hall and Seebeck effect as well as scanning capacitance spectroscopy. Both, ZCO/ZnO and ZnO/ZCO type heterostructures, showed diode characteristics. For amorphous ZCO deposited at room temperature on epitaxial ZnO/Al 2O3 thin films, we achieved current rectification ratios up to 2 × 1010, ideality factors around 2, and long-term stability.