Robust zero-watermarking is a protection of copyright approach that is both effective and distortion-free, and it has grown into a core of research on the subject of digital watermarking. This paper proposes a revolutionary zero-watermarking approach for color images using convolutional neural networks (CNN) and a 2D logistic-adjusted Chebyshev map (2D-LACM). In this algorithm, we first extracted deep feature maps from an original color image using the pre-trained VGG19. These feature maps were then fused into a featured image, and the owner's watermark sequence was incorporated using an XOR operation. Finally, 2D-LACM encrypts the copyright watermark and scrambles the binary feature matrix to ensure security. The experimental results show that the proposed algorithm performs well in terms of imperceptibility and robustness. The BER values of the extracted watermarks were below 0.0044 and the NCC values were above 0.9929, while the average PSNR values of the attacked images were 33.1537 dB. Also, it is superior to other algorithms in terms of robustness to conventional image processing and geometric attacks.