Magnetic interactions through short hydrogen bond of Cu(II)-O..D..O-Cu(II) of Natrochalcite-type compound Cu2Na(D3O2)(SO4)(2) were studied by solid-state high-resolution deuterium NMR and magnetic susceptibility measurements. A positive Weiss temperature of +9.9 K suggests a ferromagnetic interaction in a Cu(II) chain in which Cu(H) ions are linked by hydroxyl ions. Hyperfine coupling constant of deuterium in the hydrogen bond of R-O...O = 2.440 Angstrom was determined to be -1.1 MHz from temperature dependence of isotropic shift of a magic angle spinning deuterium NMR spectrum. Minus sign of the hyperfine-coupling constant indicates that negative spin is induced on the deuterium in the hydrogen bond by Cu(II) ions in both side of the O..D..O hydrogen bond. This result implies that the hydrogen bonds between the Cu(II) chains mediate a weak ferromagnetic interaction to form a two-dimensional ferromagnetically coupled Cu(II) layer. The copper layers are antiferromagnetically coupled through sodium and sulfate ions to undergo an antiferromagnetic phase transition at 3.3 K.