  We analyze theoretically the resonant inelastic x-ray scattering (RIXS) at
the Ni K edge in the stripe-ordered state of La_{2-x}Sr_xNiO_4 at x=1/3. In the
calculation of RIXS spectra, the stripe-ordered ground state is described
within the Hartree-Fock approximation by using a realistic tight-binding model
for Ni3d\gamma and O2p_{x, y} orbitals, and the electron correlations in the
electronic excitation processes are taken into account within the random-phase
approximation. The calculated RIXS spectrum shows a tail toward the low-energy
region when the momentum transfer of photons equals the stripe vector Q, being
consistent with a recent experimental result. The origin of this anomalous
momentum dependence of RIXS spectra is discussed microscopically.
