  We have studied the effect of anisotropies on the quantum phase transition of
the Kondo necklace model in dimensions D=1, 2 and 3. Both the anisotropy
$\delta$ of the inter-site interaction term and anisotropy $\Delta$ of the
on-site Kondo interaction have been included. We use a bond operator method
with constraints implemented in mean field approximation. Starting from the
paramagnetic phase we determine the critical ratio $(t/J)_c$ of the quantum
critical point and associated scaling exponents of the Kondo-singlet gap. We
show that in the case of easy-axis type anisotropy $\delta >1$ a qualitatively
new behavior in comparison to the conventional Kondo necklace model with
($\delta$,$\Delta$)=(0,1) appears. We have also obtained the antiferromagnetic
order parameter in the long range ordered phase for $t > t_c$.
