We report the first successful density functional calculation of the Co-59 chemical shift span as well as the chemical shift skew of [Co(NH3)(6)]C-3 = (243 ppm, 0.57), [Co(NH3)(4)CO3]Br = (1562 ppm, 0.30), and Co-(acac)(3) = (1115 ppm, -0.42) which agree satisfactorily with the experimental values; viz. [Co(NH3)(6)]Cl-3 = (308 ppm, 0.56), [Co(NH3)(4)CO3]Br = (1500 ppm, 0.33), and Co(acac)(3) = (1230 ppm, -0.51). We have conclusively demonstrated that hybrid HF-DFT XC functionals B3PW91 and B3LYP are more suitable for Co-59 Shielding calculation compared to the pure density functional BLYP. Furthermore, the results of this study show that the performance of the B3PW91 functional is slightly superior to the B3LYP functional. It is suggested that B3PW91/6-311+G* or B3LYP/6-311+G* is promising for Co-59 Shielding calculations.