The embodiments of the disclosure provide a method of encapsulating a flexible OLED panel and an encapsulation structure of a flexible OLED panel. The method of encapsulating a flexible OLED panel includes: forming a liquid metal layer on a first inorganic barrier layer covering the OLED device; using oxygen to oxidize the liquid metal layer, and forming a liquid metal oxide layer on a surface of the liquid metal layer; and sequentially forming an organic buffer layer and a second inorganic barrier layer on the liquid metal oxide layer to obtain an encapsulation structure. The first inorganic barrier layer, the second inorganic barrier layer, the liquid metal layer and the liquid metal oxide layer could prevent penetration of water and oxygen, and the liquid metal layer and the organic buffer layer could release the interlayer stress of the encapsulation structure in order to keep the flexibility of the encapsulation structure.