  We study constraints on additional $Z'$ bosons predicted in the
supersymmetric (SUSY) $E_6$ models by using the updated results of electroweak
experiments -- $Z$-pole experiments, $m_W$ measurements and low-energy neutral
current (LENC) experiments. We find that the effects of $Z$-$Z'$ mixing are
parametrized by (i) a tree-level contribution to the $T$-parameter, (ii) the
effective $Z$-$Z'$ mass mixing angle $\xibar$. In addition, the effect of the
direct exchange of the heavier mass eigenstate $Z_2$ in the LENC processes is
parametrized by (iii) a contact term $\contact$. We give the theoretical
predictions for the observables in the electroweak experiments together with
the standard model radiative corrections. Constraints on $T_{\rm new}$ and
$\xibar$ from the $Z$-pole and $m_W$ experiments and those on $\contact$ from
the LENC experiments are separately shown. Impacts of the kinetic mixing
between the ${\rm U(1)}_Y$ and ${\rm U(1)'}$ gauge bosons on the
$\chi^2$-analysis are studied. We show the 95% CL lower mass limit of $Z_2$ as
a function of the effective $Z$-$Z'$ mixing parameter $\zeta$, a combination of
the mass and kinetic mixings. Theoretical prediction on $\zeta$ and $g_E$ is
found for the $\chi, \psi, \eta$ and $\nu$ models by assuming the minimal
particle content of the SUSY $E_6$ models. In a certain region of the parameter
space, the $Z_2$ boson mass in the detectable range of LHC is still allowed.
