In this paper, we propose a method for processing spatiotemporal queries on semantic data streams generated from diverse sensors. On the Internet of Things (IoT) environment, the number of mobile sensors greatly increases and their locations are becoming more important. IoT services may not be fully supported when only considering the temporal feature of streaming data. Accordingly, stream processing should be performed with consideration into both temporal and spatial factors. However, existing researches have a limitation of processing spatial queries since they focus on the temporal processing of streaming data. To support spatiotemporal query processing on semantic data streams, we propose a query language, which integrates temporal and geospatial properties. Specifically, we construct a spatiotemporal index to process the proposed spatiotemporal query language efficiently. The experimental results with a prototype implementation show that the proposed method processes spatiotemporal queries in an acceptable time.