This paper describes some basic theories about the frequency selective surface (FSS). For the first time we demonstrate a novel design of a multi-band FSS to the best of our knowledge. It consists of a periodic array of concentric-square-shaped elements. Like traditional FSSs, the surface of the proposed FSS can simply be fabricated using printed circuit technology on the substrate. Simulation results show a clear dual-band and possible performance variation along with relevant parameters. We integrate this FSS into a compact 60-GHz folded dipole antenna array package in order to test its application. Results show that it successfully converts a single-band antenna to a multi-band one and specific resonant bands can be easily adjusted for the practical purposes.