In the literature of macroeconomics and the business economic press, there is a strong interest in the variation of efficiency over different times (Ray 2004). There are two methods to address this issue, such as, the Tornqvist and the Fisher productivity indexes. These two indexes use the price information of input and output factors without requiring the production technology of firms. Caves et al. (1982) introduced an index called the Malmquist efficiency index to construct a production frontier to represent the production technology of firms. Färe et al. (1992) combined ideas on the Farrell measurement and Caves et al. (1982) efficiency measurement to construct a Malmquist efficiency index directly from the input and output factors using DEA. The Malmquist efficiency index can be decomposed into two components. One component is to measure the technical change and the other component is to measure the frontier shift. In this chapter, we first illustrate the basic Malmquist index. After that, we illustrate the works of Chen and Ali (2004) to provide an extension to the Malmquist index by analyzing the above two components with an example of computer industry. Finally, a non-linear Malmquist index, proposed by Chen (2003), is discussed.