Most of the studied quantum encryption algorithms are based on square images. In this paper, based on the improved novel quantum representation of color digital images model (INCQI), a quantum color image watermarking scheme is proposed. First, INCQI improved from NCQI is used to represent the carrier and watermark images with the size 2n1×2n2 and 2n1-1×2n2-1, respectively. Secondly, before embedding, the watermarking needs to be preprocessed. That is, the watermark image with the size of 2n1-1×2n2-1 with 24-qubits color information is disordered by the fast bit-plane scramble algorithm, and then further expanded to an image with the size 2n1×2n2 with 6-qubits pixel information by the nearest-neighbor interpolation method. Finally, the dual embedded algorithm is executed and a key image with 3-qubits information is generated for retrieving the original watermark image. The extraction process of the watermark image is the inverse process of its embedding, including inverse embedding, inverse expand and inverse scrambling operations. To show that our method has a better performance in visual quality and histogram graph, a simulation of different carrier and watermark images are conducted on the classical computer's MATLAB.