In this study, Dy-doped ZnO (Zn0.8-4xDyxOy (0.05 <= x <= 0.10)) samples were prepared by the solid-state reaction method, and were characterized by using the XRD, SEM and EDX techniques. The SEM results clearly demonstrate that the grains of the samples are very well connected to each other and tightly packed. From the XRD and EDX spectra, it has been concluded that the substituting of Dy3+ for Zn2+ in ZnO causes almost no change in the hexagonal wurtzite structure of ZnO. However, the lattice parameters a and c of Dy-doped ZnO are slightly different from those of the pure ZnO. These observations may be due to the slightly different ionic sizes of Zn2+ and Dy3+ ions. Our magnetization measurements (M-H) and (M-T) show paramagnetic behavior with a negative value of the Curie-Weiss temperature, corresponding to an antiferromagnetic exchange coupling in Dy-doped ZnO. Since, for low magnetic fields the extrapolation of the H/M versus temperature curves cut the T axes at negative values, we believe that the substitution of Dy in ZnO causes an overwhelming antiferromagnetic interaction for x <= 0.10.