Abstract: Anomaly detection based on sliding window is a focus problem in data streams research.But in many cases，stream data are often transmitted over a distributed network，we must perform distributed computations to guarantee high quality results in real-time even as new data arrive.This paper firstly formalizes the problem of continuous outlier detection over distributed evolving data streams.Then two outlier measures and algorithms based on kernel density estimator are proposed which can identify outliers in a single pass.Furthermore，the experiments with synthetic datasets show that the proposed methods are both efficient and effective compared with existing outlier detection algorithms，and more suitable for data stream.