Based on random definition of economic convergence, whether convergence hypothesis is rational is tested by panel unit root method on per capita real GDP data during 1960-2003 in 99 countries and regions, the test results show that absolute convergence hypothesis is not proper for all country group, in the whole period (1960-2003), OECD countries and EU countries have obvious condition convergence phenomena, APEC countries also have significant condition convergence phenomena during 1989-2003.