Nanocrystalline Li_0.5Fe_2.5-xCr_xO₄ (2.5≤x≥0) ferrites were prepared by a sol–gel autocombustion route. X-ray diffraction was employed to confirm the cubic spinel phase formation of the ferrites. The lattice parameter decreases with increase in Cr content. The saturation magnetization, coercivity and remanance were studied as a function of Cr content. The dielectric constant and dielectric loss were measured as a function of frequency in the frequency range 20 Hz–1 MHz. Frequency dependence of dielectric constant shows dielectric dispersion due to the Maxwell–Wagner type of interfacial polarization. In order to understand the conduction mechanism, complex impedance measurements were carried out. The substitution of chromium plays an important role in changing the dielectric and magnetic properties of lithium ferrites.