A key problem in high dimensional anomaly detection is that the time spent in constructing detectors by the means of generateand-test is tolerable. In fact, due to the high sparsity. of the data, it is ineffective to construct detectors in the whole data space. Previous investigations have shown that most essentIal patterns can be discovered in different subspaces. This inspires us to construct detectors in signIficant subspaces only for anomaly detection. We first use ENCLUS-based method to discover all significant subspaces and .then use a greedy-growth algorithm to construct detectors in each subspace. The elements used to constItute a detector are gods Instead of data points, which makes the time-consumption irrelevant to the size of the nonnal data. We test the effectiveness and efficiency of our method on both synthetic and benchmark datasets. The results reveal that our method is particularly useful in anomaly detection in high dimensional data spaces.