The key challenges of global health policy are not limited to improving average health status, with a need for greater focus on reducing regional inequalities in health outcomes. This study aimed to assess health inequalities across the major Indian states used data from the Sample Registration System (SRS, 1981-2015), National Family Health Survey (NFHS, 1992-2015) and other Indian government official statistics. Catching-up plots, absolute and conditional β-convergence models, sigma (σ) plots and Kernel Density plots were used to test the Convergence Hypothesis, Dispersion Measure of Mortality (DMM) and the Gini index to measure progress in absolute and relative health inequalities across the major Indian states. The findings from the absolute β-convergence measure showed convergence in life expectancy at birth among the states. The results from the β- and σ-convergences showed convergence replacing divergence post-2000 for child and maternal mortality indicators. Furthermore, the estimates suggested a continued divergence for child underweight, but slow improvements in child full immunization. The trends in inter-state inequality suggest a decline in absolute inequality, but a significant increase or stationary trend in relative health inequality during 1981-2015. The application of different convergence metrics worked as robustness checks in the assessment of the convergence process in the selected health indicators for India over the study period.