  We investigate the spin-wave excitations in the spin-density wave state of
doped iron pnictides within a five-orbital model. We find that the excitations
along ($\pi, 0$)$\rightarrow$($\pi, \pi$) are very sensitive to the doping
whereas they do not exhibit a similar sensitivity along ($0, 0$) $\rightarrow$
($\pi, 0$). Secondly, anisotropy in the excitations around ($\pi, 0$) with an
elliptical shape grows on moving towards the hole-doped region for low energy,
whereas it decreases for the high-energy excitations on the contrary. Thirdly,
spin-wave spectral weight shifts towards the low-energy region on moving away
from zero doping. We find these features to be in qualitative agreement with
the inelastic neutron-scattering measurements for the doped pnictides.
