Orthoimage mosaicking plays an important role in remote sensing applications, such as environment monitoring and protection. However, the cloud coverage in remote sensing images often results in substantial loss of information and degradation of data quality, bringing lots of challenges to orthoimage mosaicking. Therefore, this paper proposes a flexible multi-temporal orthoimage mosaicking method based on dynamic variable patches. Different from most existing pixel-based mosaicking methods, the proposed method defines patch as the minimal processing unit for orthoimage mosaicking, and the size and position of each patch are dynamic variable. Patches from different images are rearranged under the image texture consistency constraint to generate the mosaic image. In the proposed method, the initial positions of available patches of all images are determined first, then the initial size of each patch is determined by the cloud coverage and the effective area of image. Subsequently, considering the inevitable misalignments between different orthoimages, the texture similarity between patches is utilized to select the most suitable patch, and the size of the patch is also dynamically adjusted to make the misalignments within each patch controllable. Finally, considering the color inconsistency in the overlapping areas of neighboring images, an area-weighted image blending algorithm is also presented to achieve invisible seams and smooth transitions in the final mosaic. Not only does the proposed method produce mosaic images with minimal cloud coverage areas by excluding cloud pixels as much as possible, but it is also flexible for the mosaicking of images with varying degrees of misalignments, which is achieved by dynamically adjusting the size and position of each patch while maintaining texture consistency constraint. Both simulated experiments and real data experiments are carried out to verify the performance of the proposed method. The experimental results demonstrate that the proposed method can generate the mosaic image with higher spatial continuity and radiometric consistency.