  The recent experimental data of the weak charges of Cesium and proton is
analyzed in the framework of the models based on the $\mbox{SU}(3)_C\times
\mbox{SU}(3)_L \times \mbox{U}(1)_X$ (3-3-1) gauge group, including the 3-3-1
model with CKS mechanism (3-3-1CKS) and the general 3-3-1 models with arbitrary
$\beta$ (3-3-1$\beta$) with three Higgs triplets. We will show that at the TeV
scale, the mixing among neutral gauge bosons plays significant effect. Within
the present values of the weak charges of Cesium and proton we get the lowest
mass bound of the extra heavy neutral gauge boson to be 1.27 TeV. The results
derived from the weak charge data, perturbative limit of Yukawa coupling of the
top quark, and the relevant Landau poles favor the models with $\beta =\pm
1/\sqrt{3}$ and $\beta = 0$ while ruling out the ones with $\beta= \pm
\sqrt{3}$. In addition, there are some hints showing that in the 3-3-1 models,
the third quark family should be treated differently from the first twos.
