Skyline query processing in location-based services, which considers both spatial and non-spatial attributes of the objects being queried, has recently received increasing attention. Existing solutions focus on solving point- or line-based skyline queries, in which the query location is an exact location point or a line segment. However, due to privacy consideration and limited precision of localization devices, the input of a user location is often a two-dimensional range. This paper studies a new problem on how to process such range-based skyline queries. Two novel algorithms are proposed: one is index-based (I-SKY) and the other is not based on any index (N-SKY). To handle frequent movements of the objects being queried, we also propose incremental versions of I-SKY and N-SKY, which avoid recomputing the query index and results from scratch. Additionally, we develop efficient solutions for probabilistic and continuous range-based skyline queries. Experimental results show that our proposed algorithms well outperform the baseline algorithm that simply adopts the existing line-based skyline solution. Moreover, the incremental versions of I-SKY and N-SKY save substantial computation costs, especially when the objects move frequently.