We report on the development of a new type of mode cleaner that reduces any geometric noise of the laser beam in an interferometric gravitational-wave detector. The mode cleaner is a Fabry-Perot cavity that comprises independently suspended mirrors and works as a frequency-stabilization reference as well as a mode selector; the length of the cavity is 1 m. Stand-alone tests have shown at least a 30-dB reduction in the geometric fluctuation of the beam and a 60-dB reduction of the frequency noise of the laser. We have also succeeded in operating a 20-m Fabry-Perot prototype detector (at the National Astronomical Observatory, Tokyo, Japan) by using this mode cleaner.