To reveal the energetic sequence of the alloy phases in the Co-Au system, the lattice constants, cohesive energies, and bulk modulus of the fcc Au, hcp Co, the B1, B2, and L1(0) structured CoAu phases, and the D0(3), L1(2), and D0(19) structured Co(3)Au and CoAu(3) phases, respectively, are acquired by first-principles calculations within the generalized-gradient approximation (GGA) as well as within the local density approximation (LDA). In addition, the magnetic moment of the Co atom in the studied phases are also calculated. To further examine the structural stability, the elastic constants of the studied phases are calculated and the results suggest that the fcc-type structures could be elastically stable at Co/Au = 1:3, 1:1, and 3:1, whereas the hcp-type structures could be stable at Co/Au = 1:3 and 3:1. Moreover, the spatial valence charge density (SVCD) and spin density of the studied phases are also calculated to clarify the physical origin of the structural stability. It turns out that, in the relatively stable phases, the high SVCDs mostly distribute between the similar atoms, thus forming the attractive covalent bonding to stabilize the respective structures, and that the spin density may also play an important role in influencing the stability of the ferromagnetic metastable phases.