  We report a $^{205}$Tl NMR study of vortex state for an aligned
polycrystalline sample of an overdoped high-$T_c$ superconductor
Tl$_2$Ba$_2$CuO$_{6+\delta}$ ($T_{c}\sim$85 K) with magnetic field 2 T along
the c axis. We observed an imperfect vortex lattice, so-called Bragg glass at
$T$=5 K, coexistence of vortex solid with liquid between 10 and 60 K, and
vortex melting between 65 and 85 K. No evidence for local antiferromagnetic
ordering at vortex cores was found for our sample.
