In this paper, a novel robust color image watermarking method based on Discrete Cosine Transform (DCT) and Discrete Wavelet Transform (DWT) is proposed. In this method, RGB cover image is divided into red, green and blue components. DCT and DWT are applied to each color components. Grayscale watermark image is scrambled by using Arnold transform. DCT is performed to the scrambled watermark image. Transformed watermark image is then divided into equal smaller parts. DCT coefficients of each watermark parts are embedded into four DWT bands of the color components of the cover image. The robustness of the proposed color image watermarking has been demonstrated by applying various image processing operations such as rotating, resizing, filtering, jpeg compression, and noise adding to the watermarked images. Experimental results show that the proposed method is robust to the linear and nonlinear attacks and the transparency of the watermarked images has been protected.