  There are lots of new physics models which predict an extra neutral gauge
boson, referred as Z'-boson. In a certain class of these new physics models,
the Z'-boson has flavor-dependent couplings with the fermions in the Standard
Model (SM). Based on a simple model in which couplings of the SM fermions in
the third generation with the Z'-boson are different from those of the
corresponding fermions in the first two generations, we study the signatures of
Z'-boson at the Large Hadron Collider (LHC) and the International Linear
Collider (ILC). We show that at the LHC, the Z'-boson with mass around 1 TeV
can be produced through the Drell-Yan processes and its dilepton decay modes
provide us clean signatures not only for the resonant production of Z'-boson
but also for flavor-dependences of the production cross sections. We also study
fermion pair productions at the ILC involving the virtual Z'-boson exchange.
Even though the center-of-energy of the ILC is much lower than a Z'-boson mass,
the angular distributions and the forward-backward asymmetries of fermion pair
productions show not only sizable deviations from the SM predictions but also
significant flavor-dependences.
