Retrieval of arbitrary-shaped surrounding data objects has many potential applications in spatial databases including nearby arbitrary-shaped object-of-interests retrieval surrounding a user. In this paper, we propose directional zone concept to determine directional similarity among spatial data objects. Then, we propose a novel query, called direction-based spatial skyline (DSS), which retrieves non-dominated arbitrary-shaped surrounding data objects in spatial databases for a user. The proposed DSS query is rotationally invariant as well as fair. We develop efficient algorithms for processing DSS queries in spatial databases by designing novel data pruning techniques using R-Tree data indexing scheme. Finally, we demonstrate the effectiveness and efficiency of our approach by conducting extensive experiments with real datasets.