We study hadron properties near the deconfining transition in the quenched lattice QCD simulation. This paper focuses on the heavy quarkonium states, such as $J/psi$ meson. In order to treat heavy quarks at $T>0$, we adopt the $O(a)$ improved Wilson action on anisotropic lattice. We discuss $cbar{c}$ bound state observing the wave function and compare the meson correlators at above and below $T_c$. Although we find a large change of correlator near the $T_c$, the strong spatial correlation which is almost the same as confinement phase survives even $Tsim 1.5T_c$.