Aiming at the security and efficiency of image transmission, a fast image encryption algorithm based on an improved 6-D chaotic system is proposed. Firstly, we design a hyper-chaotic system with more complex chaotic behavior, analyze the Lyapunov exponential spectrum, chaotic attractor and randomness of the system, and generate random sequences through randomness enhancement operation. Secondly, image preprocessing is used to select pixels from the original image to form a thumbnail, the size of the key space can be changed by adjusting the thumbnail. Thirdly, the hash value of the original image is used as the initial values of the hyper-chaotic system to realize the uniqueness of the key. The row encryption matrix and column encryption matrix are generated according to the maximum and minimum values of row and column pixels in the thumbnail. These two encryption matrices are composed of the full arrangement of random sequences, which refers to the random combination of random sequences in a certain order. Before the encryption, the Arnold transformation is performed on the original image and then the cipher image is obtained by row encryption and column encryption respectively. The experimental results illustrate that the proposed algorithm has excellent security performance, robustness and the speed of encryption and decryption is very fast.