Atlas construction is a crucial task for the analysis of fetal brain magnetic resonance imaging (MRI). Traditional registration-based methods for atlas construction may suffer from issues such as inaccurate registration and difficulty in defining morphology and geometric information. To address these challenges, we propose a novel deep learning-based approach for fetal brain atlas construction, which can replace traditional registration-based methods. Our fundamental assumption is that, in the feature space, the atlas is positioned at the center of a group of images, with the minimum distance to all images. Our approach utilizes the powerful representation ability of deep learning methods to learn the complex anatomical structure of the brain at multiple scales, by introducing a distance loss function to minimize the sum of distances between the atlas and all images in the group. We further utilize tissue maps as a structural guide to constrain our results, making them more physiologically realistic. To the best of our knowledge, we are the first to construct fetal brain atlases with powerful deep learning techniques. Our experiments on a large-scale fetal brain MRI dataset demonstrate that our approach can construct fetal brain atlases with better performance than previous registration-based methods while avoiding their limitations. Our code is publicly available at https://github.com/ZhangKai47/FetalBrainAtlas .