The embodiments of the invention, which belong to the field of the display technology, provide a flexible display panel and a driving method thereof, and a display apparatus. The bending curvature radius of the flexible substrate can be controlled and the power consumption is reduced. The flexible display panel comprises a pixel region, gate drive circuit regions, and a source electrode drive circuit connected with the pixel region by a chip on film. In addition, the flexible display panel also includes curvature adjusting units arranged at the two sides of the pixel region. The curvature adjusting units are formed by a plurality of isosceles-trapezoid-shaped platforms, wherein the lower surfaces of the isosceles-trapezoid-shaped platforms are successively connected; the isosceles-trapezoid-shaped platforms contain upper surfaces, lower surfaces, first waist surfaces, second waist surfaces, third waist surfaces, and fourth waist surfaces, wherein the first waist surfaces and the second waist surfaces are opposite to each other and the third waist surfaces and the fourth waist surfaces are opposite to each other. When the display panel is bent, the third waist surface of one isosceles-trapezoid-shaped platform is in contact with the fourth waist surface of the adjacent isosceles-trapezoid-shaped platform; and the upper surface of the isosceles-trapezoid-shaped platform is connected with the upper surface of the adjacent isosceles-trapezoid-shaped platform. According to the embodiments of the invention, the flexible display panel and the driving method thereof, and the display apparatus are used for manufacturing display equipment.