Active domain adaptation has emerged as a solution to balance the expensive annotation cost and the performance of trained models in semantic segmentation. However, existing works usually ignore the correlation between selected samples and its local context in feature space, which leads to inferior usage of annotation budgets. In this work, we revisit the theoretical bound of the classical Core-set method and identify that the performance is closely related to the local sample distribution around selected samples. To estimate the density of local samples efficiently, we introduce a local proxy estimator with Dynamic Masked Convolution and develop a Density-aware Greedy algorithm to optimize the bound. Extensive experiments demonstrate the superiority of our approach. Moreover, with very few labels, our scheme achieves comparable performance to the fully supervised counterpart.