In 1940 Klemm received a request from the Reich Air Ministry (RLM) chief Ernst Udet to begin work on a version of the Messerschmitt Bf 108 Taifun using wood rather than aluminium for the airframe, since the metal was then in short supply.
The wings were widened at the root and moved forward in order to accommodate additional fuel tanks, which replaced the two rear seats.
The prototype Kl 151 V1, designated with the Stammkennzeichen radio code of TB+QK, made its first flight at Böblingen on 10 September 1942, with Klemm's chief pilot Karl Voy at the controls.
On 19 February 1943 the V1 prototype was transferred to the Deutsche Versuchsanstalt für Luftfahrt ("German Experimental Institute for Aviation") at Adlershof for testing, which was successfully completed on 1 March 1943.
The problems caused by the demand for a retractable landing gear were finally solved, but the aircraft was never completed, nor put into full production.