Abstract: Recently frequency selective rasorber (FSR) has attracted growing attention since it can transmit in-band electromagnetic (EM) waves while absorbing out-of-band EM waves. They can be used to reduce bistatic radar cross section (RCS). Therefore, FSR has great potential for military applications to decrease RCS and improve their stealth performance. Firstly, recent research advances of conventional FSRs have been discussed in this paper. Then a novel FSR, called band-absorptive type FSR, has been introduced and its detailed concept has been defined. A series of band-absorptive FSRs with different performance have been presented.