Integrity assurance is an important problem for query processing in outsourced spatial databases, where the location-based service (LBS) provides query services to the clients on behalf of the data owner. If the LBS server is not trustworthy, it may return incorrect or incomplete query results intentionally or unintentionally. Therefore, to ensure the query integrity, the data owner needs to build additional authenticated data structures so that the clients can authenticate the soundness and completeness of query results. In this paper, we study the integrity assurance problem for continuous location-based skyline queries. We propose three novel techniques based on MR-Sky-tree, i.e., using valid scope, visible region, and incremental VO to reduce the computation and communication cost. Experimental results show that our proposed techniques achieve shorter computation time and lower communication cost than the existing approach.