A new kind of polarization independent electro-optic modulator is presented. The modulator needs only one piece of electro-optic crystal,and the design and the fabrication of electrodes are very simple. The propagation of light through the modulator is studied in detail using wave coupling theory of linear electrooptic effect. The study result demonstrates that the intensity of output light doesn't depend on the polarization state of the incident light. Finally,an optimum design of electro-optic crystals is given,taking examples for SBN and KNSBN which belong to 4 mm crystal system.