Aiming at the problem that hybrid domain image encryption algorithm based on chaos theory has weak encryption strength, a new image encryption algorithm based on the combination of spatial and wavelet domain was proposed. First, one-level two-dimensional discrete wavelet decomposition was performed on the original image to extract the low-frequency wavelet coefficients. Second, using the chaotic sequence generated by 2D Sine Logistic chaotic dynamic system, the low frequency sub-band was scrambled by using chaotic magic transformation, then inverse wavelet transformation was executed on decomposed image.For the scrambled image, a chaotic sequence used for encryption key in spatial domain based on intertwining Logistic map was generated, then the pixels were encrypted by using the combination technology of elemental multiplication in a Galois field with XOR. At the same time, the technology of chaotic disturbance and encryption feedback was introduced to implement one-running key. Theoretical analysis and experimental results show that the proposed algorithm has the advantages of large key space, anti-reconstruction attack, anti-differential attack, feasible encryption efficiency, strong security, and so on.