Objective To advance the goal of “Grand Convergence” in global health by 2035, this study tested the convergence hypothesis in the progress of the health status of individuals from 193 countries, using both standard and cutting-edge convergence metrics. Methods The study used multiple data sources. The methods section is categorized into two parts. (1) Health inequality measures were used for estimating inter-country inequalities. Dispersion Measure of Mortality (DMM) is used for measuring absolute inequality and Gini Coefficient for relative inequality. (2) We tested the standard convergence hypothesis for the progress in Infant Mortality Rate (IMR) and Life Expectancy at Birth (LEB) during 1950 to 2015 using methods ranging from simple graphical tools (catching-up plots) to standard parametric (absolute β and σ-convergence) and nonparametric econometric models (kernel density estimates) to detect the presence of convergence (or divergence) and convergence clubs. Findings The findings lend support to the "rise and fall" of world health inequalities measured using Life Expectancy at Birth (LEB) and Infant Mortality Rate (IMR). The test of absolute β-con-vergence for the entire period and in the recent period supports the convergence hypothesis for LEB (β = -0.0210 [95% CI -0.0227 - -0.0194], p<0.000) and rejects it for IMR (β = 0.0063 [95% CI 0.0037–0.0089], p<0.000). However, results also suggest a setback in the speed of convergence in health status across the countries in recent times, 5.4% during 1950–55 to 1980–85 compared to 3% during 1985–90 to 2010–15. Although inequality based convergence metrics showed evidence of divergence replacing convergence during 1985–90 to 2000–05, from the late 2000s, divergence was replaced by re-convergence although with a slower speed of convergence. While the non-parametric test of convergence shows an emerging process of regional convergence rather than global convergence. Conclusion We found that with a current rate of progress (2.2% per annum) the “Grand convergence” in global health can be achieved only by 2060 instead of 2035. We suggest that a roadmap to achieve “Grand Convergence” in global health should include more radical changes and work for increasing efficiency with equity to achieve a “Grand convergence” in health status across the countries by 2035.