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Objective. Medical image registration aims to find the deformation field that can align two images in a spatial position. A medical image registration method based on U-Net architecture has been proposed currently. However, U-Net architecture has few training parameters, which leads to weak learning ability, and it ignores the adverse effects of image noise on the registration accuracy. The article aims at addressing the problem of weak network learning ability and the adverse effects of noisy images on registration. Approach. Here we propose a novel unsupervised 3D brain image registration framework, which introduces the residual unit and singular value decomposition (SVD) denoising layer on the U-Net architecture. Residual unit solves the problem of network degradation, that is, registration accuracy becomes saturated and then degrades rapidly with the increase in network depth. SVD denoising layer uses the estimated model order for SVD-based low-rank image reconstruction. we use Akaike information criterion to estimate the appropriate model order, which is used to remove noise components. We use the exponential linear unit (ELU) as the activation function, which is more robust to noise than other peers. Main results. The proposed method is evaluated on the publicly available brain MRI datasets: Mindboggle101 and LPBA40. Experimental results demonstrate our method outperforms several state-of-the-art methods for the metric of Dice Score. The mean number of folding voxels and registration time are comparable to state-of-the-art methods. Significance. This study shows that Deep Residual-SVD Network can improve registration accuracy. This study also demonstrate that the residual unit can enhance the learning ability of the network, the SVD denoising layer can denoise effectively, and the ELU is more robust to noise. [ABSTRACT FROM AUTHOR]