Spatial anomalies may be single points or small regions whose non‐spatial attribute values are significantly inconsistent with those of their spatial neighborhoods. In this article, a Spatial Anomaly Points and Regions Detection method using multi‐constrained graphs and local density (SAPRD for short) is proposed. The SAPRD algorithm first models spatial proximity relationships between spatial entities by constructing a Delaunay triangulation, the edges of which provide certain statistical characteristics. By considering the difference in non‐spatial attributes of adjacent spatial entities, two levels of non‐spatial attribute distance constraints are imposed to improve the proximity graph. This produces a series of sub‐graphs, and those with very few entities are identified as candidate spatial anomalies. Moreover, the spatial anomaly degree of each entity is calculated based on the local density. A spatial interpolation surface of the spatial anomaly degree is generated using the inverse distance weight, and this is utilized to reveal potential spatial anomalies and reflect their whole areal distribution. Experiments on both simulated and real‐life spatial databases demonstrate the effectiveness and practicability of the SAPRD algorithm.