In this paper, the authors have analyzed the relationship between energy intensity gap and GDP per worker gap of China＇s western and eastern provinces over the period 1997 2006. Using panel data model with lag adjustment, taking the above provinces and six industrial sectors （agriculture, forestry, animal husbandry, and fisheries, industry, construction industry, transport, storage and post ＆ telecommunications, wholesale and retail trades ＆ catering industry, and other sectors of tertiary industry.） as the investigated subjects, the authors have conducted empirical study on the convergence of GDP per worker gap and the convergence of energy intensity gap with respect to the variation of GDP per worker gap, and have concluded that： First, the GDP per worker gap of the six industrial sectors and provinces are convergent, and of this, the convergence rate of GDP per worker gap of Construction Industry is the fastest, while that of Industry is the slowest. Second, the overall energy intensity gap between eastern and western provinces is convergent, that is, with the narrowing of GDP per worker gap between eastern and western provinces, the energy intensity gap converges, but its convergence rate is slower than that of GDP per worker gap. Third, energy intensity gap between various industrial sectors of the east and the west is either convergent or divergent, and there are differences. The energy intensity gap of agriculture, forestry, animal husbandry, and fisheries, industry, and construction industry is convergent, while that of the other three industrial sectors is divergent. Fourth, the convergence of the overall energy intensity of the western provinces is not in conformity with the convergence of the various industrial sectors, and there are significant differences, indicating that the western provinces and autonomous regions should take measures to more effectively improve their overall energy utilization efficiency at the industrial sector level.