  We study a new method for detecting non-universal gauge bosons $Z'$ via
considering their effects on rare top decays. We calculate the contributions of
the non-universal gauge bosons $Z'$ predicted by topcolor-assisted technicolor
(TC2) models and flavor-universal TC2 models on the rare top decays
$t\longrightarrow cV(V=g,\gamma,Z)$ and $t\longrightarrow cl_{i}l_{j}(l_{i},
l_{j}=\tau, \mu$, or $e)$. We show that the branching ratios of these processes
can be significantly enhanced. Over a sizable region of the parameter space, we
have $Br(t\longrightarrow cg)\sim10^{-5}$ and $Br(t\longrightarrow
c\tau\tau)\sim10^{-7}$, which may approach the observable threshold of near
future experiments. Non-universal gauge bosons $Z'$ may be detected via the
rare top decay processes at the top-quark factories such as the CERN LHC.
