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We fabricated MgB2 thin films on off-cut c-plane sapphire substrates with ZnO nanowires arranged along the edges of nanosteps to investigate the effect of two-dimensional artificial pinning centers (2D-APCs) on superconducting thin films. First, the ZnO nanowires were fabricated on the c-plane sapphire substrates with the MOCVD technique. Then, the MgB2 thin films (200 nm) were deposited on the substrates with a carrousel-type magnetron sputtering system. The AFM images and XRD (2 thetas/thetas) patterns of samples with and without ZnO nanowires show that fabricating ZnO nanowires on the substrates has a negligible effect on the crystallinity of the MgB2 thin Alms. The surface resistance (Rs) of these thin films was measured at 38 GHz with a dielectric resonator method both with and without an external dc magnetic field. A dc magnetic field of up to 2.1 T has been applied using a superconducting magnet. The Rs of the MgB2 thin films with nanowires was found to be larger than that of thin films without nanowires in the absence of external magnetic field, whereas, the Rs of the MgB2 thin films with nanowires was found to be smaller than that of those without nanowires in the external dc magnetic field from 0.7 T to 2.1 T. These results suggest that the ZnO nanowires acted as 2D-APCs.