  We examine direct limits on masses of the extra neutral gauge bosons in the
SU(4)_L \times U(1)_X model with a little Higgs mechanism confronted with the
LHC data, especially by embedding anomaly-free set of fermions. There exist two
extra neutral gauge bosons, calling Z' and Z", 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 5 TeV. For comparison, we examine the mass
limit of Z'_3 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' and Z" at the
future LHC with the center-of-momentum energy of 14 TeV. Our results can be
applicable to the models with regular Higgs mechanism if the same type of
fermion family is assigned.
