To apply the quaternion moments to the image feature extraction process and improve the performance of the image hashing algorithm, we propose a hashing algorithm based on quaternion polar complex exponential transform and image energy. First, the input color image is preprocessed to form a secondary image. The secondary image is subjected to fast quaternion generic polar complex exponential transform to obtain the mixed low-order moment coefficients as the global features of the image. Second, the algorithm extracts energy change features on the edges of the secondary image and energy point features in the center of the image as energy features of the image under the YCbCr color space. Finally, the image’s mixed low-order moment and energy features are combined and scrambled to form the final hash sequence. The experimental results show that the proposed algorithm balances robustness and differentiation well. Moreover, the hash sequence is the shortest, and the algorithm has better check-all and check-accuracy rates compared with other algorithms in the copy detection experiments.