Cartoon-texture image decomposition is about decomposing an image into the linear sum of two layers: cartoon and texture, where the key challenge is how to resolve the ambiguity between two layers. It is observed that the recurrence of texture patches occurs along multiple orientations, and the recurrence of cartoon patches only occurs along certain orientations. This paper proposes to separate these two layers by exploiting their orientation characteristics of image patch recurrence, i.e., isotropy property of texture patch recurrence versus anisotropy property of cartoon patch recurrence. Together with the sparsity-based regularizations in the image domain, a variational method is then developed in this paper for cartoon-texture decomposition. The experiments show that the proposed method noticeably outperforms many well-established ones on test images.