In recent years, with the popularization of positioning system and mobile devices, the numbers of spatial-textual objects increase extraordinarily. Location-based services using geographical information play a critical role in daily lives. Spatial keyword search has attracted more attention from academia and industry. However, many of the existing techniques can only be appliable on AND semantics. There is relatively less research supporting OR semantics. When the users do not require the exact keyword matching, the search technology that supports OR semantic is particularly important. To solve this problem, this study proposes a virtual grid-based query algorithm VGrid. VGrid is an aggregate linear quadtree (AIL) based algorithm, utilizing the easy transformation between the Morton codes and the spatial locations in the space. The algorithm can support both OR and AND semantics. Finally, a series of experiments is conducted on a real dataset, and the effectiveness and efficiency of the proposed algorithm are verified.