Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) emerged in Wuhan, China, has led to the rapid development of Coronavirus disease 2019 (COVID-19) pandemic. COVID-19 represents a fatal disease with a great global public health importance. This study aims to develop a three-parameter Weibull mathematical model using continuous functions to represent discrete COVID-19 data. Subsequently, the model was applied to quantitatively analyze the characteristics for the mortality of COVID-19, including the age, sex, the length of symptom time to hospitalization time (SH), hospitalization date to death time (HD) and symptom time to death time time (SD) and others. A three-parameter mathematical model was developed by combining the reported cases in the Data Repository from the Center for Systems Science and Engineering at Johns Hopkins University and applied to estimate and analyze the characteristics for mortality of COVID-19. We found that the scale parameters of males and females were 5.85 and 5.45, respectively. Probability density functions in both males and females were negative skewness. 5% of male patients died under the age of 43.28 (44.37 for females), 50% died under 69.55 (73.25 for females), and 95% died under 86.59 (92.78 for females). The peak age of male death was 67.45 years, while that of female death was 71.10 years. The peak and median values of SH, HD and SD in male death were correspondingly 1.17, 5.18 and 10.30 days, and 4.29, 11.36 and 16.33 days, while those in female death were 1.19, 5.80 and 12.08 days, and 4.60, 12.44 and 17.67 days, respectively. The peak age of probability density in male and female deaths was 69.55 and 73.25 years, while the high point age of their mortality risk was 77.51 and 81.73 years, respectively. The mathematical model can fit and simulate the impact of various factors on IFR. From the simulation results of the model, we can intuitively find the IFR, peak age, average age and other information of each age. In terms of time factors, the mortality rate of the most susceptible population is not the highest, and the distribution of male patients is different from the distribution of females. This means that Self-protection and self-recovery in females against SARS-CoV-2 virus might be better than those of males. Males were more likely to be infected, more likely to be admitted to the ICU and more likely to die of COVID-19. Moreover, the infection fatality ration (IFR) of COVID-19 population was intrinsically linked to the infection age. Public health measures to protect vulnerable sex and age groups might be a simple and effective way to reduce IFR.