Disclosed is a high-strength high-toughness magnesium alloy having strength and toughness practically sufficient for expanded applications of magnesium alloys. Also disclosed is a method for producing such a high-strength high-toughness magnesium alloy. Specifically disclosed is a high-strength high-toughness magnesium alloy which is characterized by containing a atom% in total of at least one metal selected from Cu, Ni and Co, and b atom% in total of at least one element selected from the group consisting of Y, Dy, Er, Ho, Gd, Tb and Tm, with a and b satisfying the following formulae (1)-(3). (1) 0.2<=a<=10; (2) 0.2<=b<=10; (3) 2/3a - 2/3 < b.