Unsupervised domain adaptation (UDA) aims at learning a classifier for an unlabeled target domain by transferring knowledge from a labeled source domain with a related but different distribution. Most existing approaches learn domain-invariant features by adapting the entire information of the images. However, forcing adaptation of domain-specific variations undermines the effectiveness of the learned features. To address this problem, we propose a novel, yet elegant module, called the deep ladder-suppression network (DLSN), which is designed to better learn the cross-domain shared content by suppressing domain-specific variations. Our proposed DLSN is an autoencoder with lateral connections from the encoder to the decoder. By this design, the domain-specific details, which are only necessary for reconstructing the unlabeled target data, are directly fed to the decoder to complete the reconstruction task, relieving the pressure of learning domain-specific variations at the later layers of the shared encoder. As a result, DLSN allows the shared encoder to focus on learning cross-domain shared content and ignores the domain-specific variations. Notably, the proposed DLSN can be used as a standard module to be integrated with various existing UDA frameworks to further boost performance. Without whistles and bells, extensive experimental results on four gold-standard domain adaptation datasets, for example: 1) Digits; 2) Office31; 3) Office-Home; and 4) VisDA-C, demonstrate that the proposed DLSN can consistently and significantly improve the performance of various popular UDA frameworks.