The key components of a polarization-independent electro-optic (EO) interferometer, including the beam splitter, mode converter, and directional coupler, are designed based on a lithium niobate (LN) platform on an integrated insulator to ensure high extinction ratios. By elaborately designing the geometric structure of the multimode interference (MMI) coupler, beam splitting of equal proportions and directional coupling of higher-order modes are realized. The most prominent characteristic of the proposed interferometer is polarization insensitivity, which is realized by converting TM polarization into TE polarization using a mode converter, providing conditions for the study of light with different polarizations. At 1550 nm, the visibility of the interferometer is 97.59% and 98.16% for TE and TM, respectively, demonstrating the high performance of the proposed LN polarization-independent interferometer.