Tb(3+)-doped zinc oxide was prepared by the co-precipitation method. The as-dried sample was annealed at 80, 300, 500, 700, and 1000 A degrees C. Rietveld analysis of the X-ray diffraction patterns of the samples annealed up to 300 A degrees C showed that all the Tb(3+) ions were entered in the ZnO lattice. But a fraction of Tb(3+) ions could not enter in the ZnO lattice above 300 A degrees C and this fraction increases with the increase of annealing temperature. The crystallite size and the internal strain due to substitution of bigger size R-ions in the ZnO lattice of the samples were estimated by using the Hall-Williamson plot. Results extracted from high resolution transmission electron microscopy are in agreement with those obtained from the XRD analysis. Magnetic susceptibility (chi) in the range of 300-14 K and magnetization as a function of magnetic field in the range of 300-5 K of the sample annealed at 80 A degrees C were measured by Faraday and SQUID magnetometers, respectively. Values of chi in the paramagnetic region were analyzed by invoking the crystal field interaction of the Tb(3+) ions with its diamagnetic neighbors. Paramagnetic to ferromagnetic phase transition has been observed at low temperature and the saturation magnetization measured at 5 K is quite high compared to the pristine sample.