The effect of a single substituted impurity spin on the spin-wave spectrum of an insulating antiferromagnet is investigated. The linear spin-wave theory of the impurity state is developed for a spin Hamiltonian including an intersublattice Heisenberg exchange term and an anisotropy energy term of the form, -DSz2. Green's function techniques are used. Both the cases of a ferromagnetically and antiferromagnetically coupled impurity spin are studied. In the numerical calculations we confine ourselves to the body-centered cubic and MnF2 (rutile)-type lattices, which are topologically equivalent to each other in the present Hamiltonian. Numerical results both of the conditions under which the s, p, d and f type localized modes appear and of the energies of these localized modes are presented for various combinations of the four parameters, α(=|J'|/J), β(=S'/S), δ(=D/Jz) and δ'(=D'/Jz). Here J and D are respectively the exchange and anisotropy constants of the host and S is a magnitude of its spin. J', D' and S' are associated with the impurity, and z is the number of nearest neighbors. It is shown that we can expect localized modes in the anisotropy energy gap as well as above and below the spin-wave energy continuum for suitable values of the parameters. The results are applied to discuss an Mn2+ impurity in the antiferromagnetic FeF2. The zero point contraction of the impurity and its nearest neighboring spins is calculated in the antiferromagnetic impurity case. It is found that, as a function of α and β, the nearest neighboring spin contraction has an oscillatory behavior.