The spinel system MgCr_xFe_2−xO₄ (x = 0.0, 0.2, 0.4, 0.6, 0.8 and 1.0) has been prepared by solid state sintering method in air at 1573 K. X-ray and neutron powder diffraction experiments have been performed on the samples at room temperature for structural characterization. Rietveld refinement of the neutron diffraction data reveals that all the samples of the series possess cubic symmetry corresponding to the space group F d-3m. The distribution of the three cations Mg, Fe and Cr over the two sublattices and other crystallographic parameters has been determined precisely. The results reveal that Cr has been substituted for Fe selectively. Cr ions invariably occupy the octahedral (B) site for all values of x. Mg and Fe ions are distributed over both A and B sites for all x values. With increasing x the occupation of Mg increases in the A site and decreases in the B site for all the samples, while the Fe ions gradually decreases in both the sites for all values of x. The lattice constant decreases with increasing Cr content in the system. The magnetic structure at room temperature was ferrimagnetic for all the samples.