  We report ^77Se-NMR measurements in the recent discovered K_0.8Fe_2Se_2 with
the superconducting transition temperature T_c=32 K. The characteristic point
of this system is that the high density of state is located in the vicinity of
the Fermi level. The comparison between Knight shift and nuclear spin lattice
relaxation rate 1/T_1 shows that the antiferromagnetic spin correlation is not
strong in this system, but it is reasonable to consider that its development
toward low temperatures occurs. 1/T_1 in the superconducting state can be
reproduced well by an s+- wave model, but a d wave model also roughly
reproduces the data. Non exponential behavior in 1/T_1 at low temperatures
disagrees with a single isotropic gap.
