Convergence concept has been often considered as income per capita convergence by the economists. Although development economics has a broad range and captures all of the dimensions of human life, development was often seen in terms of increase in the level of productivity or income. This paper extends the convergence concept to the broader measures of development and standard of living. For this purpose, a development index was constructed as an alternative to Human Development Index of United Nations Development Programme by considering the critiques that were directed to it. For the construction of this index, beside the HDI, other composite indexes about development in the literature were also evaluated in order to have a correct measure about the human development levels of countries and compare their improvement to test whether there is convergence or not for their development levels. Two types of convergence (β and σ convergence) test was constructed with the new index and results indicated that there exists a divergence in the development levels of the 95 countries in the sample for the years 1980-2013 against the results from original HDI which favors more convergence.