Spatially-resolved NMR is used to probe the magnetism in the vortex state of nearly optimally doped high-Tc cuprate Tl2Ba2CuO6+δ (Tc=85K). We found that (1) the nuclear spin-lattice relaxation rate T1-1 at 205Tl is extremely enhanced toward the vortex core and (2) T1 process become largely inhomogeneous in the vortex state and (3) the temperature dependence of T1-1 at the vortex core region shows a peak at T∼20K. These results indicates a clear evidence of the antiferromagnetic (AF) order inside the vortex core, and that the suppression of the d-wave superconducting order parameter leads to the nucleation of islands with AF order. © 2002 Elsevier Science B.V. All rights reserved.