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Change detection (CD) is one of the most vital applications in remote sensing. Recently, deep learning has achieved promising performance in the CD task. However, the deep models are task-specific and CD data set bias often exists, hence it is inevitable that deep CD models would suffer degraded performance after transferring it from original CD data set to new ones, making manually label numerous samples in the new data set unavoidable, which costs a large amount of time and human labor. How to learn a transferable CD model in the data set with enough labeled data (original domain) but can well detect changes in another data set without labeled data (target domain)? This is defined as the cross-domain change detection problem. In this paper, we propose a novel deep siamese domain adaptation convolutional neural network (DSDANet) architecture for cross-domain CD. In DSDANet, a siamese convolutional neural network first extracts spatial-spectral features from multi-temporal images. Then, through multi-kernel maximum mean discrepancy (MK-MMD), the learned feature representation is embedded into a reproducing kernel Hilbert space (RKHS), in which the distribution of two domains can be explicitly matched. By optimizing the network parameters and kernel coefficients with the source labeled data and target unlabeled data, DSDANet can learn transferrable feature representation that can bridge the discrepancy between two domains. To the best of our knowledge, it is the first time that such a domain adaptation-based deep network is proposed for CD. The theoretical analysis and experimental results demonstrate the effectiveness and potential of the proposed method.