To reduce the bandwidth and storage resources of image information in communication transmission, and improve the secure communication of information. In this paper, an image compression and encryption algorithm based on fractional-order memristive hyperchaotic system and BP neural network is proposed. In this algorithm, the image pixel values are compressed by BP neural network, the chaotic sequences of the fractional-order memristive hyperchaotic system are used to diffuse the pixel values. The experimental simulation results indicate that the proposed algorithm not only can effectively compress and encrypt image, but also have better security features. Therefore, this work provides theoretical guidance and experimental basis for the safe transmission and storage of image information in practical communication.