A broadband quasi-optical (QO) mode converter for a multifrequency gyrotron has been designed and tested at Forschungszentrum Karlsruhe (FZK). The launcher is optimized for the TE22,8 mode at 140 GHz, but the radiated beams present an almost identically focused pattern for all 9 considered modes between 105 GHz (TE17,6) and 143 GHz (TE23,8). Combining with a beam-forming mirror system, which consists of a quasielliptical mirror and two phase-correcting mirrors, further calculations show that efficiencies of more than 94% have been achieved for converting the rotating high-order cylindrical cavity modes into the usable fundamental Gaussian mode. Low power (cold) measurements show a good agreement with theoretical predictions. This QO mode converter can be used for the broadband operation of a multi-frequency 1 MW gyrotron.