To provide a high strength and high toughness magnesium alloy which has a strength and a toughness both being at a level sufficient for the alloy to be practically used corresponding to the expanded application of a magnesium alloy and a method for producing the alloy. A high strength and high toughness magnesium alloy, characterized in that it is a plastically worked product produced by a methodcomprising preparing a magnesium alloy cast product containing a atomic % of Zn, b atomic % of Y, a and b satisfying the following formulae (1) to (3), and the balance amount of Mg, subjecting the magnesium alloy cast product to a plastic working to form a preliminary plastically worked product, and it has a hcp structure magnesium phase and a long period stacking structure phase at an ordinary temperature; (1) 0.5 <= a < 5.0 (2) 0.5 < b < 5.0 (3) 2/3a - 5/6 <= b.