  In this article, the superconducting and normal state properties of TlBi$_2$
with the AlB$_2$-type structure were studied by the resistivity, magnetization
and specific heat measurements. It was found that bulk superconductivity with
$T_{C}$ = 6.2 K emerges in TlBi$_2$, which is a phonon-mediated $s$-wave
superconductor with a strong electron-phonon coupling ($\lambda$$_{ep}$ = 1.38)
and a large superconducting gap ($\Delta_{0}$/$k_{B}T_{C}$ = 2.25). We found
that the $\rho$($T$) exhibits an unusual $T$-linear dependence above 50 K, and
can be well described by the Fermi-liquid theory below 20 K. Interestingly, its
Kadowaki-Woods ratio $A/\gamma^{2}$ [9.2$\times$10$^{-5}$ $\mu\Omega$ cm(mol
K$^{2}$/mJ)$^{2}$] is unexpectedly one order of magnitude larger than that
obtained in many heavy Fermi compounds, although the electron correlation is
not so strong.
