The Cr³⁺ ions dope dmulti-oxide ZnFe_2-xCr_xO₄ ferrite nanoparticles have been synthesized by chemicalco-precipitation method. Site occupancies of Zn²⁺, Cr³⁺ and Fe³⁺ ions were analyzed using X-ray diffraction data and Buerger's method.The effect of the constituent phase ariation the magnetic hysteresis behavior was examined by saturation magnetization which decreases with thein crease in Cr³⁺ content in place of Fe³⁺ ions atoctahedral B-site. Typical blocking temperature(T_B) around 90K was observed by zero field cooling and field cooling magnetization study. Room temperature Mössbauer spectra show two paramagnetic doublets (tetrahedral and octahedral sites). The isomer shifts of both doublets decrease where as quadrupole splitting and relative area of tetrahedral A-site increases within creasing Cr³⁺ substitution. The dielectric constant (measure doncompositions x=0, 0.4,0.8 and 1.0) increases when the temperature increases as in the semiconductor. This behavior is attributed to the hopping of electrons between Fe²⁺ and Fe³⁺ ions with a thermal activation.