Automated structural damage diagnosis after earthquakes is important for improving the efficiency of disaster response and rehabilitation. In conventional data-driven frameworks which use machine learning or statistical models, structural damage diagnosis models are often constructed using supervised learning. The supervised learning requires historical structural response data and corresponding damage states (i.e., labels) for each building to learn the building-specific damage diagnosis model. However, in post-earthquake scenarios, historical data with labels are often not available for many buildings in the affected area. This makes it difficult to construct a damage diagnosis model. Further, directly using the historical data from other buildings to construct a damage diagnosis model for the target building would lead to inaccurate results. This is because each building has unique physical properties and thus unique data distribution. To this end, we introduce a new framework to transfer the model learned from other buildings to diagnose structural damage states in the target building without any labels. This framework is based on an adversarial domain adaptation approach that extracts domain-invariant feature representations of data from different buildings. The feature extraction function is trained in an adversarial way, which ensures that the extracted feature distributions are robust to changes in structures while being predictive of the damage states. With the extracted domain-invariant feature representations, the data distributions become consistent across different buildings. We evaluate our framework on both numerical simulation and field data collected from multiple building structures, which outperforms the state-of-the-art benchmark methods.