With the development of multimedia and communication technology, the protection of image copyright arises as a necessity. In the protection of copyright, image watermarking techniques are mostly used to improve robustness, invisibility, and security features. In this article, we present a novel hybrid Contourlet Transform (CT) and Discrete Cosine Transform (DCT) based blind and robust color image watermarking method to improve these features. This method is based on embedding 24-bit watermark information into an 8 x 8 image block using one-level CT and block DCT in Cb color channel of the image in YCbCr color space. In this embedding process, the DCT block is modified by using a new natural logarithm function based on the block DC coefficient. Also, a color image is used as a watermark and scrambled using Arnold transform to increase security before embedding process. The performance of the proposed method is demonstrated by applying image enhancement, geometric, and compression attacks to the watermarked images. Also, the proposed method is compared with some state-of-art methods. Experimental results illustrate that the proposed method protects the transparency of the watermarked image and has effective robustness against the attacks. The source code of this paper can be obtained from .