The invention discloses a method for preparing a nano quasi-crystal reinforced Mg-Zn-Y alloy through reciprocation extrusion. The method comprises the following steps: A, preparing cast Mg-Zn-Y alloyaccording to atom percentages of set component elements as follows: 0.5-6% of Zn, 0.08-1.2% of Y and the balance of Mg, and the content ratio of atoms of Zn and Y is (5-7):1; B, annealing the cast Mg-Zn-Y alloy for 8-20 hours at 380-420 DEG C, and performing furnace cooling; C, keeping the temperature of the annealed Mg-Zn-Y alloy at 300-400 DEG C for 2-4 hours, and performing thermal extrusion, wherein the extrusion temperature is 300-400 DEG C, and the extrusion ratio is (9-60):1; D, putting the Mg-Zn-Y alloy after thermal extrusion processing in the step C into a thermal treatment furnace,heating to 540-600 DEG C, keeping the temperature for 5-20 minutes, and performing quenching; and E, keeping the temperature of the Mg-Zn-Y alloy obtained in the step D at 200-380 DEG C for 2-4 hours,and performing reciprocation extrusion, thereby obtaining the alloy. By adopting the method, a magnesium alloy which is excellent in yield strength, tension strength and ductility can be prepared.