Neutral and anionic Co-1,Co-2(benzene)(1,2), Co-1,Co-2(pyridine)(1,2), and Co-1,Co-2(pyrimidine)(1,2) complexes have been investigated within the framework of an all-electron gradient-corrected density functional theory. The ground-state structures for each size clusters were identified based on the geometry optimization. Meanwhile, their electron affinities and vertical detachment energies were predicted and compared with the experimental values. By analyzing the pattern of highest occupied molecular orbitals (HOMOs), we found that the bond formation of these Co-organic complexes mainly arises from the 3d/4s electrons of the cobalt atoms and the pi-cloud of the organic molecules. More importantly, we presented an approach to map and analyze the Co-organic interactions from another perspective. The scatter plots of the reduced density gradient (RDG) versus rho allow us to identify the different types of interactions, and the maps of the gradient isosurfaces show a rich visualization of chemical bond and steric effects. Their magnetic properties were studied by determining the spin magnetic moments and visualizing the spin density distributions. Finally, the natural population analysis (NPA) charge was calculated to achieve a deep insight into the distribution of electron density and the reliable charge-transfer information.