A hybrid domain image encryption algorithm is developed by integrating with improved Henon map, integer wavelet transform (IWT), bit-plane decomposition, and deoxyribonucleic acid (DNA) sequence operations. First, we improve the classical two-dimensional Henon map. The improved Henon map is called 2D-ICHM, and its chaotic performance is analyzed. Compared with some existing chaotic maps, 2D-ICHM has larger parameter space, continuous chaotic range, and more complex dynamic behavior. Second, an image encryption structure based on diffusion–scrambling–diffusion and spatial domain–frequency domain–spatial domain is proposed, which we call the double sandwich structure. In the encryption process, the diffusion and scrambling operations are performed in the spatial and frequency domains, respectively. In addition, initial values and system parameters of the 2D-ICHM are obtained by the secure hash algorithm-512 (SHA-512) hash value of the plain image and the given parameters. Consequently, the proposed algorithm is highly sensitive to plain images. Finally, simulation experiments and security analysis show that the proposed algorithm has a high level of security and strong robustness to various cryptanalytic attacks.