With the rapid development of cloud services, more and more people use cloud services to store personal image privacy. However, cloud services lack security, which leads to the leakage of personal privacy. Although some scholars have proposed that images be encrypted before being uploaded to cloud services, it will cause the images to lose their availability. Recently, Zhao et al. proposed a thumbnail preserving encryption scheme, which can ensure the security of the image while maintaining the visual usability of the image, but the encryption efficiency of the algorithm is low. Therefore, this paper proposes a thumbnail preserving encryption scheme based on bit plane scrambling. In this scheme, a new one-dimensional chaotic system is proposed for the image chaos process. An improved Zigzag transformation method is proposed to change the position of pixels. The control parameters in the new one-dimensional chaotic system have a large value range, which ensures that the key space of the encryption algorithm is large enough. The improved Zigzag transformation method adds random numbers to improve the randomness of the encryption process. Experimental results show that the scheme has high encryption efficiency, and can make the encrypted image retain the visual usability of the original image, balancing security and usability.