Single crystals of the spinel-type LiMn2O4 have been successfully grown by a solvent evaporation flux method at 1173 K. The maximum size of the octahedral-shaped single crystal is 0.09 x 0.09 x 0.09 mm(3) along the octahedral edges. The single-crystal X-ray diffraction study confirmed the cubic Fd3m space group and the lattice parameter of a = 8.2483(6) Angstrom of the as-grown single crystal at 297K. The preliminary single-crystal low temperature X-ray diffraction experiments confirmed the cubic-orthorhombic structure transition around 285K on the cooling process. The tripled periodicity toward the a- and b-axis directions of the low temperature form has been also confirmed.