Juergen Rieger, the vice-president of the party that seeks to ban all immigration and sever all ties with the EU, has submitted plans to authorities in Wolfsburg - home to car giant Volkswagen - for the museum intended to "show the people what this organisation did and what it meant".
But critics have accused Mr Rieger of using the museum as a way to spread pro-Nazi propaganda.
Strength Through Joy, at one time the largest tour operator in the world, was created to promote "a National Socialist people's community and the perfection and refinement of the German people" through its tightly structured recreational programmes.
Battalions of Strength Through Joy workers built the massive holiday complex of Prora on the Baltic Sea intended to be used by 20,000 holidaying Nazi loyalists at one time. the organisation also controlled a fleet of cruise ships that allowed pre-war Germans to travel to far away destinations at rock bottom prices.
And it also financed the production of the "people's car" by VW, which later became the classic Beetle of the post-war years.
By the time war broke out, it was virtually redundant, but had accomplished its task: binding the people to Hitler and controlling leisure the way every other activity was controlled under the regime.