The forming reaction processes of magnesium aluminate spinel by a thermal decomposition of sulfate hydrate were studied with DTA, TG. SEM and X-ray powder diffraction methods. The hydrous salt composed of the mixture of the two compounds of $MgSO_4$ $6H_2O$ and ${AL_2}({SO_4})_17H_2O_3$ in which both sulfates were crystalline. On heating the hydrous slat the crystalline magnesium and aluminum sulfate anhydride to amorphous alumina magnesium sulfate anhydride decomposed to amorphous magnesia and these amorphous oxides reacted completely each other to form a spinel at $1000^{circ}C$ The apparent activation energy of forming reaction of spinel was 36.5 kcal/mole($900^{circ}C$~$1000^{circ}C$) The crystallite size of spinel obtained at $1000^{circ}C$ after 1 h was 380$AA$