During embryogenesis, cells repeatedly divide and dynamically change their positions in three-dimensional (3D) space. A robust and accurate algorithm to acquire the 3D positions of the cells would help to reveal the mechanisms of embryogenesis. To acquire quantitative criteria of embryogenesis from time-series 3D microscopic images, image processing algorithms such as segmentation have been applied. Because the cells in embryos are considerably crowded, an algorithm to segment individual cells in detail and accurately is needed. To quantify the nuclear region of every cell from a time-series 3D fluorescence microscopic image of living cells, we developed QCANet, a convolutional neural network-based segmentation algorithm for 3D fluorescence bioimages. We demonstrated that QCANet outperformed 3D Mask R-CNN, which is currently considered as the best algorithm of instance segmentation. We showed that QCANet can be applied not only to developing mouse embryos but also to developing embryos of two other model species. Using QCANet, we were able to extract several quantitative criteria of embryogenesis from 11 early mouse embryos. We showed that the extracted criteria could be used to evaluate the differences between individual embryos. This study contributes to the development of fundamental approaches for assessing embryogenesis on the basis of extracted quantitative criteria.