question: COVID-19 has spread throughout the world since 2019, and the epidemic has placed huge demands on the detection performance of COVID-19. A ParNet model is proposed in this paper which uses parameter transfer learning to initialize the training weights trained on ImageNet and then verifies its rationality from the theoretical aspect through four ways including cosine similarity, image average Hash, perceptual Hash, and difference Hash. Four ways measure image similarity from different angles. In this paper, the parallel channel and spatial attention mechanism is used to replace the channel attention mechanism, and the Swish activation function is used to replace the ReLU activation function to improve the performance of ParNet. This paper proposes ParNet to detect CT of Covid-19. Compared with the classic and the state-of-the-art models, ParNet has better performance. Source code is publicly available. © 2021, Springer Nature Switzerland AG.