  The spin excitations in the antiferromagnetic phase of half-filled Kondo
lattice model are studied by means of the decoupling approximation for spin
Green's function. The spin-wave spectrum is calculated as a function of Kondo
coupling, and this is used to calculate the thermodynamic quantities at low
temperatures. The N\'{e}el temperature of the form
  $T_{\rm N}=0.087{J}^2\ln{(1/J)}$ is obtained for the 3-dimensional case in
the weak-coupling limit. It is pointed out that the ratio of the spin-wave
velocity to the N\'{e}el temperature $v_s/T_{\rm N}$ is enhanced as the Kondo
coupling becomes small, reflecting the long-range nature of effective
interactions between localized spins.
