We report the spin Knight shift (K(s)) and the nuclear spin-lattice relaxation rate (1/T1) in the vortex state as a function of magnetic field (H) up to 28 T in the high-Tc superconductor TlSr2CaCu2O6.8 (Tc = 68 K). At low temperatures well below Tc, both K(s) and 1/T1 measured around the middle point between the two nearest vortices (saddle point) increase substantially with increasing field, which indicate that the quasiparticle states with an ungapped spectrum are extended outside the vortex cores in a d-wave superconductor. The density of states (DOS) around the saddle point is found to be kappaN(0)square root[H/H(c2)], with kappa = 0.5-0.7 and N0 being the normal-state DOS.