Iceberg Cube is meaningful for OLAP (on-line analysis processing) and compression techniques play more and more important role in reducing the storage of data warehouse and improving the efficiency of data operations. It is really a problem to compute Iceberg Cube efficiently in the compressed data warehouse. The compression techniques of data warehouse are introduced concisely in this paper, and an algorithm to compute Iceberg Cube in compressed data warehouse by mapping-complete methods is proposed. Experimental results show that this algorithm outperforms the direct method that selects Iceberg Cube tuples from the complete computed cube.