Image scrambling on classical computers has been widely studied, however, the corresponding quantum algorithms are rare. This paper proposes a block-based image scrambling scheme for the generalized model of novel enhanced quantum representation (GNEQR). It is not only suit for grayscale images and color images, but also can be used in 2n × 2m images (i.e., rectangular images). To realize the image scrambling method, we use geometric transformations and an operation of bitplane scrambling to perform position and pixel scrambling, respectively. Furthermore, the complexity of the implementation circuit of the proposed image scrambling is only O(n2) for a 2n × 2n image. Therefore, it shows our proposed quantum image scrambling is efficient. Then, the result analysis of simulation experiments demonstrates that our proposed image scrambling is effective. In addition, security analysis shows that the proposed scrambling algorithm is secure.