Cone-beam breast computed tomography (CT) provides true 3D breast images with isotropic resolution and high-contrast information, detecting calcifications as small as a few hundred microns and revealing subtle tissue differences. However, breast is highly sensitive to x-ray radiation. It is critically important for healthcare to reduce radiation dose. Few-view cone-beam CT only uses a fraction of x-ray projection data acquired by standard cone-beam breast CT, enabling significant reduction of the radiation dose. However, insufficient sampling data would cause severe streak artifacts in CT images reconstructed using conventional methods. In this study, we propose a deep-learning-based method to establish a residual neural network model for the image reconstruction, which is applied for few-view breast CT to produce high quality breast CT images. We respectively evaluate the deep-learning-based image reconstruction using one third and one quarter of x-ray projection views of the standard cone-beam breast CT. Based on clinical breast imaging dataset, we perform a supervised learning to train the neural network from few-view CT images to corresponding full-view CT images. Experimental results show that the deep learning-based image reconstruction method allows few-view breast CT to achieve a radiation dose <6 mGy per cone-beam CT scan, which is a threshold set by FDA for mammographic screening.