Cu-doped ZnO (2 wt%) thin films are deposited on p-Si (100) substrates using pulsed laser deposition (PLD) technique at room temperature. X-ray diffraction study shows the amorphous nature of these films, whereas scanning electron microscopy and atomic force microscopy images show their granular nature. A diode-like rectifying behaviour is revealed by the current-voltage characteristics of ZnO:Cu/p-Si heterojunction under both dark and light illumination conditions. In addition, it is demonstrated that there is a large enhancement in the photocurrent along with high sensitivity and responsivity of the diode. This study will be useful for the fabrication of ZnO:Cu based photodetectors.