A simple, compact, low-cost electro-optic polarization converter based on a nematic liquid crystal (LC) sandwiched between two ion-exchanged glass channel waveguides is proposed. A three-dimensional (3D) fully-vectorial (FV) finite difference beam propagation method (FDBPM) is used to simulate this optical device. The performance of the proposed polarization converter is analyzed numerically at zero and 5 V applied voltage for the case of strong anchoring of LC molecules to the surface of the waveguide. The polarization conversion efficiency is ~65% at a wavelength of 1550 nm. The total length of the directional coupler structure based converter is only 724 µm.