The work aims to propose a strongly robust dual watermark algorithm for color image based on Compressed Sensing (CS) according to the computational secrecy of CS theory, in order to solve the dispute between the robustness and transparency of the image. First, the block CS of G and B components was done to obtain the measurements after the RGB decomposition of the watermark image. Then, the NSCT decomposition of G and B components of the carrier image was carried out. LU and singular value decompositions were done after the non-overlapped blocking of the low-frequency components. The watermark measurements of each block were correspondingly embedded into the singular value matrix of the carrier according to the different embedding strengths. After a series of inverse transformations, the watermarked image was obtained. Finally, a zero watermark was generated with the block CS measurements of R component of the watermarked image, and sent to the IPR center for registration and safekeeping. Based on the water embedding and extraction simulation experiment results, the peak signal to noise ratio of the proposed algorithm was greater than 40 dB. The similarity between the reconstructed watermark image and the original image was very high. The reconstructed watermark image could resist such attacks as shearing, Gaussian noise, salt and pepper noise, Gaussian low-pass filter and JPEG compression, etc. It is concluded that, with both strong robustness and good transparency, the algorithm is simple and feasible.