The spinel system ZnxNi1-xFeCrO4 (x = 0.2, 0.4, 0.6 & 0.8) has been prepared by solid state reaction in the standard ceramic sintering method. X-ray and neutron powder diffraction experiments have been carried out on the samples at 295K. From the diffraction patterns all the samples of the series have been found to possess cubic symmetry corresponding to the space group Fd-3m. The distribution of the four cations Zn, Ni, Fe and Cr over the two sublattices, lattice parameter and oxygen position parameter have been determined precisely. The system has been found to be ferrimagnetic at room temperature.