The density functional theory (DFT)(b3p86) of Gaussian 03 has been used to optimize the structure of the Co2molecule, a transition metal element molecule. The result shows that the ground state for the Co2 molecule is a 7-multiple state, indicating a spin polarization effect in the Co2 molecule. Meanwhile, we have not found any spin pollution because the wavefunction of the ground state is not mingled with wavefunctions of higher-energy states. So for the ground state of Co2 molecule to be a 7-multiple state is the indicative of spin polarization effect of the Co2molecule, that is, there exist 6 parallel spin electrons in a Co2 molecule. The number of non-conjugated electrons is the greatest. These electrons occupy different spacial orbitals so that the energy of the Co2 molecule is minimized. It can be concluded that the effect of parallel spin in the Co2 molecule is larger than the effect of the conjugated molecule,which is obviously related to the effect of electron d delocalization. In addition, the Murrell-Sorbie potential functions with the parameters for the ground state and the other states of the Co2 molecule are derived. The dissociation energy De for the ground state of Co2 molecule is 4.0489eV, equilibrium bond length Re is 0.2061 nm, and vibration frequency 11.2222 aJ.nm-4respectively(1 a.J=10-18 J). The other spectroscopic data for the ground state of Co2 molecule ωexe,Be, and αe are 0.7202 cm-1, 0.1347 cm-1, and 2.9120× 10-1 cm-1 respectively. And ωexe is the non-syntonic part of frequency, Be is the rotational constant, αe is revised constant of rotational constant for non-rigid part of Co2 molecule.