  The critical properties of the frustrated Kondo necklace model with a half
saturation magnetization ($m=1/2$) have been studied by means of an
exact-diagonalization method. It is shown from bosonization technique that the
model can be effectively expressed as a quantum sine-Gordom model. Thus it may
show three (dimer plateau, N{\'e}el plateau and Tomonaga-Luttinger liquid)
phases due to competitions among the Ising anisotropy $\Delta$, and the
nearest- and next-nearest-neighbor exchange interactions $J_1$ and $J_2$. The
boundary lines on the $\Delta-J_2/J_1$ phase diagram separating the three
phases are determined by the method of level spectroscopy based on the
conformal field theory.
