  The top quark is the heaviest particle to date discovered, with a mass close
to the electroweak symmetry breaking scale. It is expected that the top quark
would be sensitive to the new physics at the TeV scale. One of the most
important aspects of the top quark physics can be the investigation of the
possible anomalous couplings. Here, we study the top quark flavor changing
neutral current (FCNC) couplings via the extra gauge boson Z' at the Large
Hadron Collider (LHC) and the Compact Linear Collider (CLIC) energies. We
calculate the total cross sections for the signal and the corresponding
Standard Model (SM) background processes. For an FCNC mixing parameter x=0.2
and the sequential Z' mass of 1 TeV, we find the single top quark FCNC
production cross sections 0.38(1.76) fb at the LHC with sqrt{s_{pp}}=7(14) TeV,
respectively. For the resonance production of sequential Z' boson and decays to
single top quark at the Compact Linear Collider (CLIC) energies, including the
initial state radiation and beamstrahlung effects, we find the cross section
27.96(0.91) fb at sqrt{s_{e^{+}e^{-}}}=1(3) TeV, respectively. We make the
analysis to investigate the parameter space (mixing-mass) through various Z'
models. It is shown that the results benefit from the flavor tagging.
