Fabry-Perot interferometers have been widely studied and used for well over a century. However, they have always been treated as stationary devices in the past. In this Letter, we investigate the optical transmission of a longitudinally moving Fabry-Perot interferometer within the framework of relativity and establish a general relation between the transmission coefficient and the velocity for uniform motions. Several features of the transmission spectrum are analyzed, with special attentions given to the non-relativistic regime, where application prospects are evaluated. New, to the best of our knowledge, potential interferometric schemes, such as velocity-scanning interferometry and hybrid interferometers based on nested configurations, are proposed. Finally, a special case of non-uniform motion is also investigated.