The invention relates to a high-strength and high-toughness magnesium alloy containing Sc and a preparation method thereof. The high-strength and high-toughness magnesium alloy comprises the followingcomponents of, by weight, 4.5-6.5% of Y, 1.5-4.0% of Nd, 1.5-4.0% of Gd, 0.05-0.5% of Sc and 0.15-1.5% of Zr, the balance being Mg, wherein the total amount of rare earth elements is not more than 10wt%. The high-strength and high-toughness magnesium alloy is divided into Mg-Y-Nd-Gd-Sc-Zr, precipitation strengthening of rare earth containing intermetallic compounds as the main strengthening mechanism, the nucleation density in the solidification process of the material is improved by adding a non-rare earth element Sc, and the alloy structure is further refined significantly. The material hasquite good indoor temperature and high temperature mechanical properties, and meanwhile, high plasticity among similar materials is achieved. The invention further provides a preparation method of the high-strength and high-toughness magnesium alloy containing the Sc.