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Cross-database micro-expression recognition (CDMER) is a difficult task, where the target (testing) and source (training) samples come from different micro-expression (ME) databases, resulting in the inconsistency of the feature distributions between each other, and hence affecting the performance of many existing MER methods. To address this problem, we propose a dual-stream convolutional neural network (DSCNN) for dealing with CDMER tasks. In the DSCNN, two stream branches are designed to study temporal and facial region cues in ME samples with the goal of recognizing MEs. In addition, in the training process, the domain discrepancy loss is used to enforce the target and source samples to have similar feature distributions in some layers of the DSCNN. Extensive CDMER experiments are conducted to evaluate the DSCNN. The results show that our proposed DSCNN model achieves a higher recognition accuracy when compared with some representative CDMER methods.