With the extensive recent development of communication methods and resulting increase in data surveillance and espionage, the need for reliable data encryption methods is greater than ever. Conventional encryption calculations, for example, DES and RSA, are not beneficial in the field of picture encryption because of some inherent characteristics of pictures such as bulk data size and high redundancy, which are problematic for conventional encryption. Many researchers have proposed different image encryption schemes to overcome image encryption problems. In the last two decades, more and more studies have looked to incorporate conventional encryption methods and the complex behavior of chaotic signals. In this paper, a novel image encryption algorithm is proposed based on pixel chaotic permutation. A chaotic logistic map and Ikeda map are used to design a new pseudo-random bit generator, and a novel permutation scheme is used to modify pixel values. Then, a new permutation algorithm based on a traditional Japanese game called Amidakuji is used for pixel scrambling. Different statistical manners, such as correlation coefficient, NPCR (Number of Pixels Change Rate), UACI (Unified Average Changing Intensity), and entropy, are used to provide analysis of the effectiveness of the proposed encryption methods. Our example reveals that the proposed encryption method can obtain highly secure encrypted images using a novel chaotic permutation method based on Amidakuji.