  An extension of the Standard Model to the local gauge group $SU(3)_c\otimes
SU(4)_L\otimes U(1)_X$ as a three-family model is presented. The model does not
contain exotic electric charges and we obtain a consistent mass spectrum by
introducing an anomaly-free discrete $Z_2$ symmetry. The neutral currents
coupled to all neutral vector bosons in the model are studied. By using
experimental results from the CERN LEP, SLAC Linear Collider and atomic parity
violation we constrain the mixing angle between two of the neutral currents in
the model and the mass of the additional neutral gauge bosons to be
$-0.0032\leq\sin\theta\leq 0.0031$ and $0.67 \hbox{TeV}\leq M_{Z_2} \leq 6.1$
TeV at 95% C.L., respectively.
