A high-strength magnesium-based alloy possessing a microcrystalline composition represented by the general formula: Mg.sub.a Al.sub.b M.sub.c or Mg.sub.a,Al.sub.b M.sub.c X.sub.d (wherein M stands for at least one element selected from the group consisting of Ga, Sr, and Ba, X stands for at least one element selected from the group consisting of Zn, Ce, Zr, and Ca, and a, a', b, c, and d stand for atomic percents respectively in the ranges of 78.ltoreq.a.ltoreq.94, 75.ltoreq.a'.ltoreq.94, 2.ltoreq.b.ltoreq.12, 1.ltoreq.c.ltoreq.10, and 0.1.ltoreq.d.ltoreq.3). This alloy can be advantageously produced by rapidly solidifying the melt of an alloy of the composition shown above by the liquid quenching method. It is useful as high-strength materials and highly refractory materials owing to its high hardness, strength, and heat-resistance. It is also useful as materials with high specific strength because of light weight and high strength.