We have studied electronic and magnetic structures of K0.8+xFe1.6Se2 by performing the first-principles electronic structure calculations. The ground state of the Fe-vacancies ordered K0.8Fe1.6Se2 is found to be a quasi-two-dimensional blocked checkerboard antiferromagnetic (AFM) semiconductor with an energy gap of 594 meV and a large ordering magnetic moment of 3.37 µB for each Fe atom, in excellent agreement with the neutron scattering measurement. The underlying mechanism is the chemical-bonding-driven tetramer lattice distortion. K0.8+xFe1.6Se2 with finite x is a doped AFM semiconductor with low conducting carrier concentration which is approximately proportional to the excess potassium content, consistent qualitatively with the infrared observation. Our study reveals the importance of the interplay between antiferromagnetism and superconductivity in these materials. This suggests that K0.8Fe1.6Se2, instead of KFe2Se2, should be regarded as a parent compound from which the superconductivity emerges upon electron or hole doping. The recent discovery of high-Tc superconductivity in potassium intercalated FeSe[1] and other iron-based chalcogenides [2,3] has triggered a surge of interest for the investigation of unconventional superconducting pairing mechanism. In particular, it was found that the superconductivity in these materials coexists with a strong antiferromagnetic (AFM) order with an unprecedentedly large magnetic moment of 3.31 µ B /Fe formed below a Neel temperature of 559K [4,5], meanwhile the conducting electron concentration is extremely low [6]. Unlike the collinear [7][8][9] or bi-collinear[10-12] AFM order observed in the parent compounds of other iron-based superconductors, the neutron observation found that these materials have a blocked checkerboard AFM order [5].These compounds have the ThCr 2 Si 2 type crystal structure, as shown in Fig.