Accurate measurement of fish’s features is of great significance for breeding management and decision-making. Fish body area, body length, and body width are important features for judging the growth status of fish in smart aquaculture. These features can be used as an important reference for bait feeding, fishing, and classification. In view of the fact that fish body is usually inclined on actual production line, this research proposes a scheme based on U-Net and fish morphological characteristics to segment and precisely measure the features of inclined fish. Firstly, the data set is processed and expanded through data enhancement such as contrast transformation and rotation transformation. This operation can simulate the real shooting environment and enhance robustness of the training model. Secondly, U-Net is introduced. Using the expanded training set to generate a segmentation model. Trained model is used to segment the test samples to generate accurate segmented images and output fish body area. Finally, by combining fish morphological characteristics, the inclined angle of the fish body is determined. After rotation correction, circumscribed rectangle method is adopted to obtain the body length and width of fish in the image. The experimental results show that using the proposed scheme, the mIoU of test set is as high as 0.974, the relative error of average fish body area is only 1.25%, the relative error of average fish body length is only 0.65%, and the relative error of average fish body width is only 0.84%. Compared with traditional circumscribed rectangle method, the relative error of body length is reduced by 5.25%, and the relative error of body width is reduced by 39.87%.