Nanocrystalline samples of lithium manganese oxide with cubic spinel structure have been prepared by combustion of reaction mixtures containing Li(I) and Mn(II) nitrates that operate as oxidisers, and sucrose that acts as fuel. The samples were characterised by X-ray diffraction, transmission electron microscopy, thermal analysis, and impedance and electrochemical measurements. The effect of the fuel content on the purity and morphology of the products was analysed. The samples as prepared showed small amounts of Mn2O3 and Mn3O4 as impurities, depending on the amount of sucrose used in the synthesis. Annealing at 700 °C led to single-phase cubic spinels. In these phases, the smallest average particle size (ca. 30 nm) corresponded to the sample obtained with a hyperstoichiometric amount of fuel. This sample showed the Li1.05Mn1.95O4 composition as deduced from the thermal and electrochemical data. No variation in conductivity associated with the cubic⇔orthorhombic phase transition was observed. The electrochemical behaviour as positive electrode showed good cyclability at high current densities (reversible capacity of 73 mAh g−1 at 2.46 mA cm−2).