The binary forsterite($Mg_2SiO_4$)/spinel ($MgAl_2O_4$) system, a possible refractory for industrial applications, is investigated for their density and grain growth the same firing conditions as the each component material between $1400^{circ}C$ and $1700^{circ}C$ ($1650^{circ}C$). The forsterite grain growth exponent is established to be equal to 5 for all compositions within this binary system. Generally; the spinel addition to forsterite inhibited the forsterite grain growth. The activation energies for the forsterite grain growth of the eight compositions(weight ratio of forsterite/spinel) within the binary system are determined to be: 952$pm$79(95/5), 363$pm$37(90/10), 219$pm$21(80/20), 220$pm$44(70/30), 112$pm$16(50/50), 112$pm$23(30/70), 198$pm$26(10/90), and 121$pm$12(5/95) KJ/mol. The more forsterite is contained within the binary system, the higher value the activation energy for forsterite grain growth. It is considered that the forsterite grain growth at the higher forsterite compositions are more inhibited by spinel than that of the lower forsterite compositions.