In order to reduce domain discrepancy to improve the performance of cross-domain spoken language identification (SLID) system, as an unsupervised domain adaptation (UDA) method, we have proposed a joint distribution alignment (JDA) model based on optimal transport (OT). A discrepancy measurement based on OT was adopted for JDA between training and test data sets. In our previous study, it was supposed that the training and test sets share the same label space. However, in real applications, the label space of the test set is only a subset of that of the training set. Fully matching training and test domains for distribution alignment may introduce negative domain transfer. In this paper, we propose an JDA model based on partial optimal transport (POT), i.e., only partial couplings of OT are allowed during JDA. Moreover, since the label of test data is unknown, in the POT, a soft weighting on the coupling based on transport cost is adaptively set during domain alignment. Experiments were carried out on a cross-domain SLID task to evaluate the proposed UDA. Results showed that our proposed UDA significantly improved the performance due to the consideration of the partial couplings in OT.