  We study the low-lying excitations in 5d transition-metal oxide Sr_2IrO_4 on
the localized electron picture. We find that Hund's coupling together with the
spin-orbit interaction leads to exchange anisotropy which causes the spin wave
gap. Introducing the isospin operators acting on Kramers' doublet in Ir atoms,
we derive the effective spin Hamiltonian from a multi-orbital Hubbard model
with the t_{2g} orbitals in the square lattice. We introduce the Green's
functions including the anomalous type for the boson operators by expanding the
spin operators in terms of boson operators in the lowest order of 1/S, and
solve the coupled equations of motion for those functions. Two modes are found
to emerge with slightly different energies, in contrast to the spin waves in
the isotropic Heisenberg model. At the $\Gamma$-point, one mode has the zero
excitation energy while another has a finite energy. They have the same
excitation energy at the M point, but still have different energies at the X
point.
