  The parity violation in cesium atom is analysed in the framework of the
models based on the SU(3)_C X SU(3)_L X U(1)_N gauge group. It is shown that in
the minimal version, the main contribution to a deviation of weak charge \Delta
Q_W due to direct Z' exchange is negative. New data on parity violation in the
cesium atom seems not favour to the minimal version, while it gets a positive
value in the version with right-handed neutrinos. We obtain a bound on the $Z'$
mass at a range from 1.4 TeV to 2.6 TeV. The allowed regions for the
Z-Z'$mixing angle are also derived.
