This paper proposes a blind and robust color image watermarking method based on a new three-dimensional Hénon chaotic map and uses integer wavelet transform, discrete wavelet transform and contourlet transform in embedding and extracting processes. In the presented approach, color images are divided into main nonoverlapping parts, and one of the transforms is applied to these parts. Then the low–low sub-band of transform is selected. The suggested map is used to find blocks in the embedding process. The bits of watermark are embedded in the parts of images to increase the robustness of the proposed watermarking scheme. To improve the quality of the final watermark, the suggested technique uses a correction process in the extracting process. In this paper, the bifurcation diagram, Lyapunov exponent, cobweb plot and trajectory diagram are used to show the chaotic behavior of the proposed map. Based on DIEHARD, ENT and NIST test suites, the suggested map can be used as a pseudo-random number generator. The simulation results show that the proposed watermarking algorithm is robust against most image processing attacks like salt & pepper, cropping, low-pass filter, wiener filter, blurring, etc. The comparison results between the suggested watermarking scheme, and some similar methods show that the presented technique has good performance, imperceptibility, acceptable robustness and outperforms most related methods.