Applying density functional theory (DFT) calculations, we predict the structural and electronic properties of different types of palladium–fullerene polymers. We examine the structures of one- (1-D), two- (2-D), and three-dimensional (3-D) polymers. We find that the most stable polymer is that represented by bonding via the [6,6] position of the fullerene molecules with Pd in a distorted tetrahedral coordination. Special attention is paid to the electronic structure. We demonstrate clearly that changes in the Pd coordination geometry strongly affect the projected density-of-states picture of the 4d orbitals. The energy band gaps in the 1-D and 2-D systems obviously differ from that in the 3-D one; thus, we can directly modify the electronic properties of polymers. The results at the AM1* level of theory for the reduced 1-D polymer show that isolated polarons are the preferred electronic states.