The invention discloses a method of preparing a nano quasi-crystal reinforced Mg-Zn-Y alloy by two times of extrusion. The method comprises the following steps that A, an as-cast state Mg-Zn-Y alloy is prepared according to set atom percentage contents of various component elements, wherein the various component elements are as follows, 0.5-6% of Zn, 0.08-1.2% of Y and the balance Mg, and a ratioof the atom percentage content of Zn to the atom percentage content of Y is (5-7):1; B, the as-cast state Mg-Zn-Y alloy is subjected to annealing at 380-420 DEG C for 8-20 h, and furnace cooling is carried out; C, the Mg-Zn-Y alloy subjected to the annealing is subjected to heat preservation at 300-400 DEG C for 2-4 h, then hot extrusion is carried out with the extrusion temperature being 300-400DEG C and the extrusion ratio being (9-60):1; D, the Mg-Zn-Y alloy obtained after being subjected to the hot extrusion in the step C is placed in a heat treatment furnace, is heated to 540-600 DEG C and is subjected to heat preservation for 5-20 min, and quenching is carried out; and E, the Mg-Zn-Y alloy obtained in the step D is subjected to heat preservation at 300-400 DEG C for 2-4 h, and thensecondary hot extrusion is carried out, thus the nano quasi-crystal reinforced Mg-Zn-Y alloy is obtained. The method can prepare a high-performance magnesium alloy which is excellent in yield strength, tensile strength and elongation percentage.