In the microwave band, Optical Electric Field Sensors (OEFS) provide an attractive method to measure electromagnetic fields precisely. It is difficult however, to develop an OEFS that operates with both wide bandwidth and high sensitivity. In this paper, we propose a Log-Periodic Dipole antenna Array (LPDA)-type OEFS that achieves high sensitivity over a wide bandwidth. The LPDA-type OEFS has a large number of electrodes that are attached to each of the antenna elements. Not only the lengths of the antenna elements but also the lengths of electrodes vary log-periodically. The OEFS responds to microwaves by synchronizing the propagation direction of light with the propagation direction of the microwave. An OEFS constructed of y-cut z-propagation Lithium Niobate (LN) demonstrates good stability against temperature variation. Theoretical analysis with respect to the refractive index variation and optical modulator with the crystal orientation will be provided in this paper. In addition, the characteristics of the proposed LPDA-type OEFS will be shown over wide bandwidth in the microwave band.