Nanocrystalline spinel lithium manganese oxide ($LiMn_2O_4$) powders with narrow-size-distribution, pure-phase particles, and high crystallinity with an average crystallite size of about 70 nm were synthesized at $600^{circ}C$ for 6 h in air by freeze drying method. Spinel $LiMn_2O_4$ is also prepared by sol-gel using citric acid as a chelating agent. The influence of different parameters such as pH conditions, solvent, molar ratio of citric acid to total metal ions, calcination temperature, starting material on the structure, morphology and purity of this oxide was investigated. The results of sol-gel method show that pure $LiMn_2O_4$ with average crystallite size of about 130 nm can be produced from nitrate salts as starting materials at $800^{circ}C$ for 6 h in air. The optimum pH and molar ratio of chelating agent to total metal ions are $4{leq}pH{leq}6$ and 1.0, respectively. A possible mechanism on the formation of the nanocrystallines synthesized by sol-gel was also discussed. At the end a comparison of the differences between two methods was made on the basis of x-ray diffraction (XRD), scanning electron microscopy (SEM), Fourier transform infrared spectroscopy (FTIR), and thermogravimetric analysis (TGA) tests.