We systematically investigate the interactions and magnetic properties of a series of 3d transition-metal (TM; Sc–Ni) atoms adsorbed on perfect graphene (G6), and on defective graphene with a single pentagon (G5), a single heptagon (G7), or a pentagon–heptagon pair (G57) by means of spin-polarized density functional calculations. The TM atoms tend to adsorb at hollow sites of the perfect and defective graphene, except for G6Cr, G5Cr, and G5Ni. The binding energies of TMs on defective graphene are remarkably enhanced and show a V-shape, with GNCr and GNMn having the lowest binding energies. Furthermore, complicated element- and defect-dependent magnetic behavior is observed in GNTM. Particularly, the magnetic moments of GNTM linearly increase by about 1 μB and follow a hierarchy of G7TM<G57TM<G5TM as the TM varies from Sc to Mn, and the magnetic moments begin to decrease afterward; by choosing different types of defects, the magnetic moments can be tuned over a broad range, for example, from 3 to 6 μB for GNCr. The intriguing element- and defect-dependent magnetic behavior is further understood from electron- and back-donation mechanisms.