The low frequency quadratic electro optical effect with a maximum electro optical coefficient of g = 8 × 10 -19 m 2 /V 2 (i.e., four orders of magnitude greater than the standard high frequency value) has been studied in thin films of ferroelectric polymer PVDF(70%)-TrFE(30%). The observed effect is related to the process of spontaneous polarization switching, during which the electron oscillators of C-F and C-H dipole groups rotate to become parallel to the applied field. As a result, the ellipsoid of the refractive index exhibits narrowing in the direction perpendicular to the field. The field dependence of the electro optical coefficient g correlates with that of the apparent dielectric permittivity, which can be introduced under the condition of ferroelectric polarization switching. The observed electro optical effect strongly decreases when the fre quency increases up to several hundred hertz. The temperature dependence of the effect exhibits clearly pro nounced hysteresis in the region of the ferroelectric phase transition.