Detecting anomalies with high accuracy and real time from large amounts of streaming data is a challenge for many real-world applications, such as smart city, astronomical observations, and remote sensing. This article focuses on a special kind of stream, catalog stream, whose high-level catalog structure can be used to analyze the stream effectively. We first formulate the anomaly detection in catalog streams as a constrained optimization problem based on a catalog stream matrix. Then, a novel filtering-identifying based anomaly detection algorithm (FIAD) is proposed, which includes two complementary strategies, true event identifying and false alarm filtering, data oriented general method and domain oriented specific method together, to detect truly valuable anomalies. Furthermore, different kinds of attention windows are developed to provide corresponding data for various algorithm components. A scalable and lightweight catalog stream processing framework CSPF is designed to support and implement the proposed method efficiently. A prototype system is developed to evaluate the proposed algorithm. Extensive experiments are conducted on the catalog stream data sets from an operational super large field-of-view high-cadence astronomy observation. The experimental results show that the proposed method can achieve a false-positive rate as low as 0.04%, reduces the false alarms by 98.6% compared with the existing methods, and the latency to handle each catalog is 2.1 seconds (much less than the required 15 seconds). Furthermore, a total of 36 transient candidates, including seven microlensing events, 27 superflares, and two dual-superflares, are detected from 21.67 million stars (involving 1.09 million catalogs) from one observation season.