  We study the phenomenology of a massive graviton $G$ with non-universal
couplings to the Standard Model (SM) particles. Such a particle can arise as a
warped Kaluza-Klein graviton from a framework of the Randall-Sundrum
extra-dimension model. In particular, we consider a case in which $G$ is
top-philic, i.e., $G$ interacts strongly with the right-handed top quark,
resulting in the large top-loop contributions to its production via the gluon
fusion and its decays to the SM gauge bosons. We take into account the
constraints from the current 13 TeV LHC data on the channels of $t\bar{t}$,
$\gamma\gamma$, $jj (gg)$, $\gamma Z$, and $ZZ$. Consequently, it is found that
the strongest limit for this spin-2 resonance $G$ comes from the $t\bar{t}$
pair search, which constrains the cutoff scale to be of ${\cal O}$(100 GeV) for
the right-top coupling of ${\cal O}(1)$ and the massive graviton mass in the
range $m_G$=2-5 TeV, significantly relaxed compared with the universal $G$
coupling case.
