New times of minima of the W UMa-type eclipsing binary FZ Orionis, obtained at the Athens University Observatory, have been used together with all reliable timings found in the literature in order to study the period variation and search for the presence of a third body in the system. Its O-C diagram is presented and apparent period changes are discussed with respect to possible Light-Time Effect (LITE) in the system. New improved LITE elements, orbital periods and minimum mass of potential third body are given.