Melt foaming method is one of cost-effective methods to make metal foam and it has been successfully applied to fabricate Mg foams. In this research, AZ31 Mg alloy ingot was used as a metal matrix, using AlCa granular as thickening agent and $CaCO_3$ powder as foaming agent, AZ31 Mg alloy foams were fabricated by melt-foaming method at different foaming temperatures. The porosity was above 41.2%~73.3%, pore size was between 0.38~1.52 mm, and homogenous pore structures were obtained. Microstructure and mechanical properties of the AZ31 Mg alloy foams were investigated by optical microscopy, SEM and UTM. The results showed that pore structure and pore distribution were much better than those fabricated at lower temperatures. The compression behavior of the AZ31 Mg alloy foam behaved as typical porous materials. As the foaming temperature increased from $660^{circ}C$ to $750^{circ}C$, the compressed strength also increased. The AZ31 Mg alloy foam with a foaming temperature of $720^{circ}C$ had the best energy absorption. The energy absorption value of Mg foam was 15.52 $MJ/m^3$ at a densification strain of 52%. Furthermore, the high energy absorption efficiencies of the AZ31 Mg alloy foam kept at about 0.85 in the plastic plateau region, which indicates that composite foam possess a high energy absorption characteristic, and the Vickers hardness of AZ31 Mg alloy foam decreased as the foaming temperature increased.