The intrinsic mechanical and interfacial characteristics of precipitates in Mg–Sn–Y alloys were calculated to predict strengthening precipitates and to design novel Mg alloys. The first-principle calculations results indicated that the Sn3Y5 phase had a higher bulk and shear moduli than the Mg24Y5 and Mg2Sn phases. The Mg/Sn3Y5 interface was more stable and possessed a higher adhesive strength than the Mg/Mg2Sn and Mg/Mg24Y5 interfaces. Four as-cast alloys (S10Y3 (Mg-0.5Sn-0.16Y), S5Y3 (Mg-0.43Sn-0.25Y), S1Y1 (Mg-0.36Sn-0.37Y) and S3Y5 (Mg-0.27Sn-0.48Y) alloy (at.%)) were then designed according to the different Sn to Y atomic ratios (10:3, 5:3, 1:1 and 3:5). The lower Sn to Y atomic ratio promoted the formation of the Sn3Y5 phase in the S3Y5 alloy, whereas the S10Y3 alloy with a higher Sn to Y atomic ratio mainly consisted of the Mg2Sn phase. Compared with the S10Y3 alloy, the yield strength and ultimate tensile strength of the S3Y5 alloy were increased by 70% and 16% without sacrificing the elongation at room temperature, which was greatly improved by 127% and 104% at elevated temperatures simultaneously. These results suggested that the calculations of intrinsic mechanical and interfacial characteristics of precipitates may provide an effective tool to design high-strength Mg alloys.