It is challenging to quantitatively clarify the determining medical and social factors of COVID-19 mortality, which varied by 2-3 orders of magnitude across countries. Here, we present evidence that the whole-cycle patterns of mortality follow a logistic law for 52 countries. A universal linear law is found between the ICU time in the early stage and the most important quantity regarding the epidemic: its duration. Saturation mortality is found to have a power law relationship with median age and bed occupancy, which quantitatively explains the great variation in mortality based on the two key thresholds of median age (=38) and bed occupancy (=15%). We predict that deaths will be reduced by 36% when the number of beds is doubled for countries with older populations. Facing the next wave of the epidemic, this model can make early predictions on the epidemic duration and medical supply reservation.