Accurate segmentation of the brain into major tissue types, e.g., the gray matter, white matter, and cerebrospinal fluid, in magnetic resonance (MR) imaging is critical for quantification of the brain anatomy and function. The availability of 7T MR scanners can provide more accurate and reliable voxel-wise tissue labels, which can be leveraged to supervise the training of the tissue segmentation in the conventional 3T brain images. Specifically, a deep learning based method can be used to build the highly non-linear mapping from the 3T intensity image to the more reliable label maps obtained from the 7T images of the same subject. However, the misalignment between 3T and 7T MR images due to image distortions poses a major obstacle to achieving better segmentation accuracy. To address this issue, we measure the quality of the 3T-7T alignment by using a correlation coefficient map. Then we propose a cascaded nested network (CaNes-Net) for 3T MR image segmentation and a multi-stage solution for training this model with the ground-truth tissue labels from 7T images. This paper has two main contributions. First, by incorporating the correlation loss, the above mentioned obstacle can be well addressed. Second, the geodesic distance maps are constructed based on the intermediate segmentation results to guide the training of the CaNes-Net as an iterative coarse-to-fine process. We evaluated the proposed CaNes-Net with the state-of-the-art methods on 18 in-house acquired subjects. We also qualitatively assessed the performance of the proposed model and U-Net on the ADNI dataset. Our results indicate that the proposed CaNes-Net is able to dramatically reduce mis-segmentation caused by the misalignment and achieves substantially improved accuracy over all the other methods.