A magnesium (Mg) solid solution with a long periodic hexagonal structure was found in a Mg97Zn1Y2 (at.%) alloy in a bulk form prepared by warm extrusion of atomized powders at 573 K. The novel structure has an ABACAB-type six layered packing with lattice parameters of a = 0.322 nm and c = 3 × 0.521 nm. The Mg solid solution has fine grain sizes of 100 to 150 nm and contains 0.78 at.% Zn and 1.82 at.% Y. In addition, cubic Mg24Y5 particles with a size of about 7 nm are dispersed at small volume fractions of less than 10% in the Mg matrix. The specific density (ρ) of the extruded bulk Mg–Zn–Y alloy was 1.84 Mg/m3. The tensile yield strength (σy) and elongation (δ) are 610 MPa and 5%, respectively, at room temperature, and the specific yield strength defined by the ratio of σy to ρ is as high as 3.3 × 105 Nm/kg. High σy values exceeding 400 MPa are also maintained at temperatures up to 473 K. It is noticed that the σy levels are 2.5 to 5 times higher than those for conventional high-strength type Mg-based alloys. The Mg-based alloy also exhibits a high-strain-rate superplasticity with large δ of 700 to 800% at high strain rates of 0.1 to 0.2 s−1 and 623 K. The excellent mechanical properties are due to the combination of the fine grain size, new long periodic hexagonal solid solution containing Y and Zn, and dispersion of fine Mg24Y5 particles. The new Mg-based alloy is expected to be used in many fields.