The purpose of this study is to propose a new economic index, namely, real national income average growth rate (RNIAGR), which measures the performance of economic growth with consideration for income distribution. This study also develops another new economic index, called five-scale real national income average growth rate (FSRNIAGR), which simplifies the calculation of RNIAGR. The merits of these new indexes are discussed to justify their efficacy. This paper also justifies the use of proposed index by showing that this index can actually measure the ordering of social welfare. To highlight the difference between this new index and the traditional ones, this paper compares the index with real economic growth rate using the data of Taiwan. In addition, this paper shows that when the real growth stagnates or even declines, this new index indicates that income distribution deteriorates.