The invention relates to a Cu-bearing heat-resistance rare earth magnesium alloy pertaining to the metal material technology field and a preparation method thereof, the magnesium alloy comprises Cu and at least one alloy element of element composed of Y, Gd, Sm, Nd, La, Ce, Tb, Dy, Ho, Er and Tm, wherein, the atomic percent of copper is a, the total atomic percent of the alloy element is b, and the residual quantity are Mg and impurities, wherein, a and b meet that: a is equal to or more than 0.1 and equal to or less than 5, and b is equal to or more than 0.5 and equal to or less than 5. The preparation of the magnesium alloy comprises a melting process and a follow-up heat treatment process, the magnesium alloy can be taken as cast magnesium alloy and deformation magnesium alloy, and has better mechanical properties such as room-temperature, hot strength and the like than traditional WE series commercial magnesium.