[en] We examine the direct limits on masses of extra neutral gauge bosons in the $SU{(4)}_L\times <!--\; ??\; -->U{(1)}_X$ model with a little Higgs mechanism confronted with the Large Hadron Collider (LHC) data, especially by embedding an anomaly-free set of fermions. There exist two extra neutral gauge bosons, called $Z^{\mathrm{\prime <!--\; ???\; -->}}$ and $Z^{\mathrm{\prime <!--\; ???\; -->}\mathrm{\prime <!--\; ???\; -->}},$ in this model. The lower exclusion limit of the mass of the lighter extra neutral gauge boson is about 3 TeV, while that of the heavier one is 5 TeV. For comparison, we examine the mass limit of the $Z_3^{\mathrm{\prime <!--\; ???\; -->}}$ boson in the $SU{(3)}_L\times <!--\; ??\; -->U{(1)}_X$ model as well and discuss the implication of our result in the $SU{(4)}_L\times <!--\; ??\; -->U{(1)}_X$ model with a standard Higgs mechanism. We also discuss the discovery potential of $Z^{\mathrm{\prime <!--\; ???\; -->}}$ and $Z^{\mathrm{\prime <!--\; ???\; -->}\mathrm{\prime <!--\; ???\; -->}}$ at the future LHC with a center-of-momentum energy of 14 TeV. Our results can be applicable to models with a regular Higgs mechanism if the same type of fermion family is assigned. (paper)