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.
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