A backlight module for curved liquid crystal display device and a curved liquid crystal display device are disclosed. The backlight module comprises a backplate, a light guide plate and a backlight source that are arranged in the backplate, and quantum tubes that are arranged between the light guide plate and the backlight source, wherein a fold line which matches a curved surface of the curved liquid crystal display device is formed by the quantum tubes. In the backlight module according to the present disclosure, the fold line that is formed by the quantum tubes can be fitted into a curved line so as to match the curved surface of the curved liquid crystal display device. The quantum tubes can be applied to the curved liquid crystal display device through this arrangement, whereby the color purity of the curved liquid crystal display device can be improved, and the color gamut thereof can be enlarged.