Stable p‐type ZnO thin films on sapphire (0001) and n‐type 4H‐SiC (0001) substrates were achieved in low‐ionized oxygen pressure using radical‐source laser molecular beam epitaxy system. The p conduction type of ZnO films originates from not only zinc vacancy, but also interstitial oxygen acceptor defects, which was investigated by X‐ray diffraction, atomic force microscopy, X‐ray photoelectron spectroscopy, and photoluminescence measurements. The electrical properties were tested 180 days after deposition by Hall measurement. For the ZnO thin film grown on sapphire, a stable mobility of 17.0 cm2 V−1s−1, a resistivity of 1.08 Ωcm, and a hole concentration of 3.4 × 1017 cm−3 were achieved. The selection of 4H‐SiC substrates improved the crystalline quality of ZnO films confirmed by the X‐ray diffraction patterns. An intrinsic p‐type ZnO film on n‐type 4H‐SiC, with a stable mobility of 44.6 cm2 V−1s−1, a resistivity of 1.02 Ωcm, and a hole concentration of 1.4 × 1017 cm−3 were achieved. The current–voltage curve of the p–n ZnO homojunction shows typical diode characteristics, which also confirmed the achievement of the p‐type ZnO. The current–voltage curve of the p‐ZnO/n‐4H‐SiC heterojunction also shows p–n junction rectifier features. These results suggest the possibility of ultraviolet photodetectors and light‐emitting devices.