Effect of Co substitution on crystal structures of two nickel silicides, NiSi and $NiSi_2$, is investigated by using an ab initio calculation. Relaxed NiSi and $NiSi_2$ structures are calculated and the calculated lattice parameters are in good agreement with experimentally determined lattice parameters within about 2%. A Co atom substitutes a Ni and Si site, respectively, to evaluate the preferable site between them. Co prefers Ni site to Si site in both NiSi and $NiSi_2$. The calculated total energy also indicates that the Co substitution to Ni site stabilizes both the NiSi and $NiSi_2$ structures. Co also prefers Ni site in $NiSi_2$ to that in NiSi, indicating that $NiSi_2$ becomes more stable than NiSi with Co substitution. As Co addition to NiSi improves its thermal stability experimentally, this indicates that the energy barrier between the two phases is high enough to prevent the phase transformation from NiSi to $NiSi_2$ up to high temperature.