Generation capacity and market trading volume by private generation companies were less than 1% in 2001, however it reached up to 15% at the end of 2001. This sharp increase of market share by private sector is generally considered desirable, but could raise concerns of market power in the electricity industry. This study suggests two new indices to measure market power both in the market level and at firm level. Following Borenstein, Bushnell and Wolak (2002), we estimate the level of market power using data at firm level. Our estimation results using 2006 data suggest that the level of market power at market level is higher during summer than other seasons in 2006. In addition, this study suggests a new index to measure the level of market power at firm level, which is the relationship between market share of inframarginal firms and their frequency. This index implies that large firms tend to frequently determine the SMPs during the lower demand periods, while small firms tend to set the SMPs during higher demand periods.