Obtaining a highly synergistic strength and elongation in cast magnesium (Mg) alloys at low cost is a chronic problem. A series of low-cost and high strength cast Mg–7Zn-xAl-0.3Mn (x = 1, 3, 5) alloys (labeled as ZAM710, ZAM730, and ZAM750 alloys, respectively) were designed based on the phase diagram simulation and prepared successfully by electric resistance furnace. The present results showed that the as-cast ZAM710 alloy was composed of α-Mg, MgZn, AlMn, and Al8Mn5 phases. The MgZn phase disappeared and the Mg32(Al, Zn)49 phase formed as the Al content increased to more than 3 wt%. In addition, with the increase of Al content, the volume fraction of the second phase increased and the grain was refined. The microstructures and mechanical properties of these alloys were improved after heat treatment. Among them, the transmission electron microscopy analysis showed that there were a large number of nanometer precipitation strengthening phases in the aged ZAM750 alloy. One was a rod-shaped Mg4Zn7 phase and the other was a disk-shaped MgZn2 phase. The comprehensive mechanical properties of the ZAM750 alloy were most outstanding, and the tensile strength, yield strength, and elongation were 309.4 MPa, 202.0 MPa, and 6.1%, respectively. The strengthening mechanism of the ZAM750 alloy mainly included grain boundary strengthening and precipitation strengthening, and the contribution values to the yield strength of the ZAM750 alloy were 95.8 MPa and 75.7 MPa, respectively. This work can provide some guidance and new design ideas for the development of low-cost and high-strength cast Mg alloys.