This study examines a two-country tax competition model, in which the capital endowment and income inequality are asymmetric in each country. Hwang and Cheo [1] and Peralta and van Ypersele [2] show that when countries differ in capital endowments, the country with the higher capital endowment sets a lower capital tax rate. However, their studies assume that all inhabitants are homogeneous. We extend the models of the two aforementioned studies and conduct an analysis taking into account the asymmetry in income inequality within countries. The tax rate is set by the policy maker elected by majority voting in each country's election. We find that a higher tax rate may be set in the country with higher capital endowment under certain conditions. Further, if the income inequality is sufficiently large, the median voters in each country unambiguously delegate the right to decide the tax rate to residents who prefer a higher tax rate than their own, regardless of the capital endowments of the two countries.Additionally, globalization affects the social situation around the world. In particular, the widening of income inequality and the poverty of developed countries is a serious problem. OECD [3] shows that the share of the richest 1% in all pre-tax income has more than doubled since 1980, reaching almost 20% in 2012. This trend has also been observed in other developed countries. These international (in developing vs. developed countries) and intra-national (income inequality) asymmetries may influence the policies implemented by the politicians. In developed countries with large tax base, politicians who decide lower tax rates may be elected in order to prevent the outflow of the tax base. On the other hand, in countries with large income inequality, politicians who decide higher tax rates may be elected as many of the population prefer more income redistribution and public services. Baldwin and Krugman [4] show that the average corporate tax rate (total corporate tax revenue divided by GDP) has increased between the 1980s and 2000 in European countries. We may be able to explain the cause of this trend as the widening of income inequality. Therefore, in this study, we conduct an analysis taking into account these two asymmetries, and clarify how each asymmetry affects the tax rate of each country. Recent trends suggest that tax competition research considering these asymmetries has important implications for theoretical and empirical analysis.