The identification of the local community structure in geo-social networks has been gaining increasing attention. The structure of geo-social networks evolves over time with the addition/deletion of edges/nodes and the update of node locations, which has motivated recent studies to mine local communities in dynamic geo-social networks. Mining communities in evolving geo-social networks is essential for understanding the evolution of group behaviors. However, in most previous studies on the community mining in dynamic networks, local spatial-aware communities were not identified in evolving geo-social networks. Therefore, in this study, the problem of determining local spatial-aware communities in evolving geo-social networks is proposed. To address this problem, we propose a parameter-free algorithm, called LSADEN. Specifically, LSADEN involves two main steps: i) selecting candidate nodes, where LSADEN defines the community dominance relation under dynamic environments to obtain candidate nodes that improve the community in terms of the community quality or the smoothness between communities at adjacent time stamps; ii) community expansion, where LSADEN designs the Manhattan distance of communities to add some candidate nodes to the local community. Experimental results on six real-world datasets and one synthetic dataset show that LSADEN performs well both in terms of the quality of communities and the smoothness between communities at adjacent time stamps.