The New Vacuum Solar Telescope (NVST) is the largest solar telescope in China. When using CCDs for imaging, equal-thickness fringes caused by thin-film interference can occur. Such fringes reduce the quality of NVST data but cannot be removed using standard flat fielding. In this paper, a correction method based on multi-scale decomposition and adaptive partitioning is proposed. The original image is decomposed into several sub-scales by multi-scale decomposition. The region containing fringes is found and divided by an adaptive partitioning method. The interference fringes are then filtered by a frequency-domain Gaussian filter on every partitioned image. Our analysis shows that this method can effectively remove the interference fringes from a solar image while preserving useful information.