To cater to fault diagnosis of rotating machinery under complex working conditions, unsupervised domain adaptation technology has been widely explored and applied. Existing methods mainly reduce domain bias in two ways, including metric learning and discriminator-based adversarial learning. Different from these technologies, in this work, we only resort to entropy optimization strategies and develop a novel entropy-oriented domain adaptation (EODA) model for intelligent diagnosis of rotating machinery. Specifically, a convolutional network with a cosine-distance classifier is introduced to construct the model framework, which can reduce intraclass variation and make the output more confident. In addition, negentropy-guided prediction diversity optimization and minimax entropy game-guided prototype-feature alignment are co-designed to realize domain adaptation. Extensive experiments based on two different mechanical systems are used to validate our method. Comprehensive results and discussions demonstrate that our EODA can achieve compelling performance.