Charge density study of a mixed-valence tri-cobalt compound, Co-3(mu-admtrz)(4)(mu-OH)(2)(CN)(6)center dot 2H2O (1) (admtrz = 3,5-dimethyl-4-amino-1,2,4-triazole), is investigated based on high resolution X-ray diffraction data and density functional theory (DFT) calculations. The molecular structure of this compound contains three cobalt atoms in a linear fashion, where two terminal ones are Co-III at a low-spin (LS) state and a central one is Co-II at a high-spin (HS) state with a total spin quantum number, S-total, of 3/2. It is centrosymmetric with the center of inversion located at the central Co atom (Co2). The Co2 ion is linked with each terminal cobalt (Co1) ion through two mu-admtrz ligands and a mu-OH ligand in a CoN4O2 coordination, where the Co1 is bonded additionally to three CN ligands with CoN2OC3 coordination. The combined experimental and theoretical charge density study identifies the different characters of two types of cobalt ions; more pronounced charge concentration and depletion features in the valence shell charge concentration (VSCC) are found in the Co-III ion than in the Co-II ion, and d-orbital populations also show the difference. According to topological properties associated with the bond critical point (BCP), the Col-C(N) bond is the strongest among all the Co-ligand bonds in this compound; the Co-O is stronger than Co-N bond. Again Col-O is stronger than Co2-O, so as the Co1-N being stronger than Co2-N bond. The electronic configuration of each type of Co atom is further characterized through magnetic measurement, Co-specific X-ray absorption near edge spectroscopy (XANES), and X-ray emission spectra (XES).