The effect of alloy composition on the glass forming ability (GFA) of the Ca-rich Ca-Mg-Zn alloys has been investigated in $Ca_{65}Mg_{5+x}Zn_{30-x}$ and $Ca_{55+x}Mg_{15}Zn_{30-x}$ (x=0, 5, 10, 15, 20) alloys. In a wide composition range of 15-25% Zn and 10-20% Mg bulk metallic glass (BMG) samples with the diameter larger than 6 mm are fabricated by conventional copper mold casting method in air atmosphere. Among the alloys investigated, the $Ca_{65}Mg_{15}Zn_{20}$ alloy exhibits the highest GFA enabling to form BMG sample with the diameter of at least 15 mm. The crystalline phase formed during solidification of $Ca_{65}Mg_{15}Zn_{20}$ ($D_{max}=15;mm$) could be identified as a mixture of $Ca_3Zn$ and $CaMg_2$ cause by the redistribution of the constituent elements on long-range scale. The compressive fracture strength and fracture elongation of the $Ca_{65}Mg_{15}Zn_{20}$ BMG are 602 MPa and 2.08% respectively. The ${sigma}$ parameter which has been recently proposed for evaluating GFA exhibits better correlation with GFA of Ca-Mg-Zn alloys than other parameters suggested so far such as ${Delta}T_x$, $T_{rg}$, K, ${gamma}$, and ${Delta}T^*$ parameters.