A high strength aluminum-based alloy, which having a composition of the general formula: Al.sub.bal Q.sub.a M.sub.b X.sub.c T.sub.d, wherein Q represents at least one element selected from the group consisting of Mn, Cr, V, Mo and W; M represents at least one element selected from the group consisting of Co, Ni, Cu and Fe; X represents at least one element selected from rare earth elements including Y or Mm; T represents at least one element selected from the group consisting of Ti, Zr and Hf; and a, b, c and d represent the following atomic percentages: 1.ltoreq.a.ltoreq.7, 0>5, 0>c.ltoreq.5 and 0>d.ltoreq.2, and contains quasi-crystals in the structure thereof. The alloy of the present invention is excellent in the hardness and strength at both room temperature and a high temperature, and also in thermal resistance and ductility. In addition, it is usable as a high specific strength material having a high strength and a low specific gravity due to a small amount of addition of rare earth element or elements.