Deformable registration has been widely used in neuroscience studies for spatial normalization of brain images onto a standard space. Due to high anatomical variances across individual brains, registration performance could be limited when trying to estimate entire deformation pathway either from template to subject or subject to template. Symmetric image registration offers an effective way to simultaneously deform template and subject images towards each other until they meet at the middle point. Although some intensity-based registration algorithms have nicely incorporated this concept of symmetric deformation, the intensity matching between two images may not necessarily imply the correct matching of anatomical correspondences. In this paper, we integrate both strategies of hierarchical attribute matching and symmetric diffeomorphic deformation for building a new symmetric-diffeomorphic registration algorithm for MR brain images. The performance of our proposed method has been extensively evaluated and further compared with top-ranked image registration methods (SyN and diffeomorphic Demons) on brain MR images. In all experiments, our registration method achieves the best registration performance, compared to all other state-of-the-art registration methods.