We explore theoretically impurity states in the antiferromagnetic spin-density wave state of the iron arsenide. Two types of impurity models are employed: one has only the intraband scattering while the other has both the intraband and interband scattering with the equal strength. Interestingly, the impurity bound state is revealed around the impurity site in the energy gap for both models. However, the impurity state is doubly degenerate with respect to spin for the first case; while the

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... impurity state is observed in either the spin-up or spin-down channel for the second one. The impurity-induced variations of the local density of states are also examined.