The epidemic curve of COVID-19 for the first two years of the pandemic clearly shows a sequential peak structure with a constant half width, despite various levels of preventive measures implemented in many countries and various infection strengths of each coronavirus variant. However, previous epidemic models have not been able to explain this phenomenon. Here we show the mechanism causing this peak structure and the universality of the half width of the peak by means of a self-consistent approach that we have developed. Comparison with the data of all peaks observed in 15 countries strongly suggests that convergence of the epidemic peak is achieved when all susceptible people estimated by the self-consistent approach are infected. This directly causes the universality of the half width. The present approach also provides a method to quantitatively evaluate the effects of various prevention measures and has the ability to predict the peak position and height from the data of the strength of infection in the initial stage of each pandemic peak.