  The doping dependence of spin excitations in
Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ is studied based on a two-orbital model
under RPA approximation. The interplay between the spin-density-wave (SDW) and
superconductivity (SC) is considered in our calculation. Our results for the
spin susceptibility are in good agreement with neutron scattering (NS)
experiments in various doping ranges at temperatures (T) above and below the
superconducting transition temperature T$_{c}$. For the overdoped sample where
one of the two hole pockets around $\Gamma$ point disappears according to
ARPES, we show that the imaginary part of the spin susceptibility in both SC
and normal phases exhibits a gap-like behavior. This feature is consistent with
the "pseudogap" as observed by recent NMR and NS experiments.
