Three single crystals of CaTi2O4 (CT)-type, CaFe2O4 (CF)-type, and new low-density CaFe2O4 (LD-CF) related MgAl2O4 were synthesized at 27 GPa and 2500 °C and also CT-type MgAl2O4 at 45 GPa and 1727 °C using conventional and advanced multi-anvil technologies, respectively. The structures of CT-type and LD-CF related MgAl2O4 were analyzed by single-crystal X-ray diffraction. The lattice parameters of the CT-type phases synthesized at 27 and 45 GPa were a = 2.7903(4), b = 9.2132(10), and c = 9.3968(12) Å, and a = 2.7982(6), b = 9.2532(15), and c = 9.4461(16) Å, respectively, (Z = 4, space group: Cmcm) at ambient conditions. This phase has an AlO6 octahedral site and an MgO8 bicapped trigonal prism with two longer cation-oxygen bonds. The LD-CF related phase has a novel structure with orthorhombic symmetry (space group: Pnma), and lattice parameters of a = 9.207(2), b = 3.0118(6), and c = 9.739(2) Å (Z = 4). The structural framework comprises tunnel-shaped spaces constructed by edge- and corner-sharing of AlO6 and a 4+1 AlO5 trigonal bipyramid, in which MgO5 trigonal bipyramids are accommodated. The CF-type MgAl2O4 also has the same space group of Pnma but a slightly different atomic arrangement, with Mg and Al coordination numbers of 8 and 6, respectively. The LD-CF related phase has the lowest density of 3.50 g/cm3 among MgAl2O4 polymorphs, despite its high-pressure synthesis from the spinel-type phase (3.58 g/cm3), indicating that the LD-CF related phase formed via back-transformation from a high-pressure phase during the recovery. Combined with the previously determined phase relations, the phase transition between CF-and CT-type MgAl2O4 is expected to have a steep Clapeyron slope. Therefore, CT-type phase may be stable in basaltic- and continental-crust compositions at higher temperatures than the average mantle geotherm in the wide pressure range of the lower mantle. The LD-CF related phase could be found in shocked meteorites and used for estimating shock conditions.