Analytic window query is a commonly used query in the relational databases. It answers the aggregations of data over a sliding window. For example, to get the average prices of a stock for each day. However, it is not supported in the spatial databases. Because the spatial data are not in a one-dimension space, there is no straightforward way to extend the original analytic window query to spatial databases. But these queries are useful and meaningful. For example, to find the average number of visits for all the POIs in the circle with a fixed radius for each POI as the centre. In this paper, we define the aggregate analytic window query over spatial data and propose algorithms for grid index and tree-index. We also analyze the complexity of the algorithms to prove they are efficient and practical.