Consumer price index (CPI) is an important basis for nation to analysis the macroeconomic situation , to investigate the level of inflation, and to the formulate macroeconomic policy. It's also significant for macroeconomic analysis and forecasting to use the scientific and rational way for the CPI compilation. Statisticians over the past two hundred years put forward a number of index for different purposes A slight change of the formula or methodology which causes the nuances of the consumer price index may have a significant financial impact. Therefore, the consumer price index method is very important not only in theory, but also in practice. Elementary price index is the basic elements of the consumer price index, the quality of consumer price index depends largely on the quality of the primary index. This paper describes three basic price index and compare the differences between them. Superlative index is widely used because it approximates the cost of living index, this article compares the key differences between the three Superlative index. Finally, combined with the current situation of China's CPI compilation, a few suggestions to improve it is proposed.
KEYWORDS：CPI， Price index， Elementary price index，Superlative index number
