Domain adaptation (DA) has achieved a resounding success to learn a good classifier by leveraging labeled data from a source domain to adapt to an unlabeled target domain. However, in a general setting when the target domain contains classes that are never observed in the source domain, namely in Open Set Domain Adaptation (OSDA), existing DA methods failed to work because of the interference of the extra unknown classes. This is a much more challenging problem, since it can easily result in negative transfer due to the mismatch between the unknown and known classes. Existing researches are susceptible to misclassification when target domain unknown samples in the feature space distributed near the decision boundary learned from the labeled source domain. To overcome this, we propose Joint Partial Optimal Transport (JPOT), fully utilizing information of not only the labeled source domain but also the discriminative representation of unknown class in the target domain. The proposed joint discriminative prototypical compactness loss can not only achieve intra-class compactness and inter-class separability, but also estimate the mean and variance of the unknown class through backpropagation, which remains intractable for previous methods due to the blindness about the structure of the unknown classes. To our best knowledge, this is the first optimal transport model for OSDA. Extensive experiments demonstrate that our proposed model can significantly boost the performance of open set domain adaptation on standard DA datasets.