Using the density functional theory (DFT) under both frameworks of the local density approximation (LDA) and the generalized gradient approximation (GGA), we show that the anomalous magnetic moment of Tb-n (n = 2-20, 22, 33) clusters found in recent experiment [J. AppL Phys. 2010, 107, 09B526] is due to the antiferromagnetic or ferromagnetic couplings between Tb atoms in dusters. The local spin magnetic moment of Tb atoms is in the range 5.1-5.7 mu(B), which is faintly influenced by the cluster sizes, geometrical structures, and spin arrangements. Emphasis is made on the Tb-13 cluster to eliminate the large magnetic discrepancy between the experiment and calculation. Geometrical evolution shows that the square-antiprism motif with one centered atom is competitive with the icosahedral motif for small Tb clusters n = 9-12, whereas the 0 close packed icosahedral growth is clearly favored for large clusters n = 13-20, 22, 33. The clusters containing 4, 7, 10, 13, and 19 atoms are found to be more stable than their neighboring sizes, in agreement with the early mass spectral measurements. The electronic properties including the HOMO-LUMO energy gaps, ionization potentials, electron affinities, and electric dipole moments are calculated, and more importantly, the variational trends of the magnetic moment and electric dipole moment qualitatively fit well with the experimental observations.