Chromium substituted polycrystalline Yttrium Iron Garnets (Y3Fe5-xCrxO12 with x=0 to 0.5) were prepared in single-phase form with lattice constant in the range of 12.3775 angstrom to 12.3560 angstrom. All samples exhibit ferrimagnetic transition with transition temperature (T-c) in the range of 547K for x=0 to 494K for x=0.5. The saturation magnetization value at room temperature is found to increase with Cr concentration that is, from 24.8 to 26.6emu/g and this is attributed to the preferential occupation of Cr3+ ions at octahedral site of Fe3+ ions. The frequency dependence of impedance data shows the relaxation and thermal activation of charge carriers across grains and grain boundaries. The complex impedance spectra were modeled by considering equivalent circuits having contributions from the resistance and constant phase element due to grains and grain boundaries and capacitance across grain boundaries. The dielectric constant is found to increase from 20 to 52 as the Cr concentration is increased and it is attributed to hopping of charge carriers across Fe2+-Fe3+ centers. The Arrhenius plots of relaxation time of charge carriers and conductivity show an anomaly in the vicinity of ferrimagnetic transition temperature and it highlights the presence of magneto-electric coupling.