Nanocrystalline ZnMn^1-xCr_xFeO₄ (1.0 ≥ x ≥ 0) ferrites were synthesized by sol–gel technique. X-ray diffraction (XRD) confirmed the formation of single phasic cubic spinel lattice for all the compositions studied. Lattice parameter shows a decreasing trend with an increase in Cr content in the compositions. Formation of spherical nanoparticles was revealed by scanning electron microscopy (SEM) analysis. Infrared spectroscopic studies revealed two main absorption bands in the range 400–800 cm^-1 arising due to tetrahedral (A) and octahedral (B) site vibrations. Dielectric constant, dielectric loss tangent, ac conductivity and complex impedance were measured as a function of frequency in the range 20 Hz to 1 MHz. Frequency dependence of dielectric constant shows dielectric dispersion due to the Maxwell–Wagner type of interfacial polarization. The role of chromium in modifying structural and dielectric properties of these ferrites has been explained.