High quality n-ZnO/p-SiC heterojunction diodes have been fabricated and their photoresponse properties have been investigated. X-ray diffraction (XRD) θ-2θ patterns show that highly c-axis oriented ZnO films were epitaxially grown on 4H-SiC. The RMS roughness is observed as low as 2 nm by atomic force microscope (AFM). Current-voltage (I-V) characteristics of the fabricated heterojunction diodes have a good rectifying characteristics, and a leakage current less than 10-9 A at -10 V, with a forward current of ∼10-5 A at +10 V. The responsivity is measured for different UV wavwlengths. As the intensity of UV wavelength is decreased from 365 nm to 254 nm, the photocurrent increased 1.7x10-5 A to 3x10-5 A.