The invention discloses a flexible solar cell module and a preparation method and application thereof. The flexible solar cell module comprises upper skin, a first packaging adhesive film, a flexible solar cell array, a second packaging adhesive film, a supporting member, a third packaging adhesive film, and lower skin in a hot-pressing packaging in order from up to down, and the supporting member is a polymethacrylimide foam board. The preparation method comprises the steps of stacking the upper skin, the first packaging adhesive film, the flexible solar cell array, the second packaging adhesive film, the supporting member, the third packaging adhesive film, and the lower skin in order from up to down, and performing lamination. The flexible solar cell module is advantaged by low surface density, good bending and flexibility, suitability for being attached to airfoil curved surface, good reliability, no packaging problems such as warping, fragmentation, etc., and wide application in spacecrafts such as solar unmanned aerial vehicles, etc.