Open Set Domain Adaptation (OSDA) aims to reduce the variation across domains while distinguishing between known samples and unknown samples. However, existing OSDA methods are based on deep neural network classifiers to separate unknown samples, which leads the network to produce overconfident predictions and fails to establish the boundary between the known and the unknown. We propose an Energy-based Open Set Domain Adaptation method (EOS). Specifically, EOS is a new two-stage approach of separation followed by alignment. We use an energy-based anomaly detection strategy as a separation method for unknown samples, transforming the traditional K-way classification task into a K+1-dimensional classifier that uses an additional dimension to model the uncertainty of Out-of-distribution (OOD) samples. Then, we use a coarse-to-fine separation method to continuously adjust the separation results and add the exact separation results as weights in the alignment process, weighing their importance to the feature distribution alignment. In the alignment phase we also optimize our separation network module at the same time, so that the module can be better adapted with invariant features. We have done experiments on the standard ground Office-31, Office-Home, and VisDA-2017 benchmarks, and the results show that our approach outperforms our competitors in most cases.