To solve the overlapping search of multidimensional spatial database containing large quantity of objects with dynamic spatial extent, this paper proposes an index structure named Space Grid Tree (SG-Tree) based on Peano Space-Filling Curve (SFC) to index the region of object. By appropriate linearization strategy, the bounding box of a spatial object can be presented by a union of mutually disjoint hypercube grids with different granularity, and only the object’s oid, i.e. the identifier which is used to refer to this object in the database, is registered on the nodes relative to these grids. The overlapping queries of spatial objects can be operated real-time directly on SG-Tree. Experiments show that SG-Tree is feasible and efficient to solve the overlapping search of multidimensional spatial objects.