Controlling the spread of SARS-CoV-2 will require high vaccination coverage, but acceptance of the vaccine could be impacted by perceptions of vaccine safety and effectiveness. The aim of this study was to characterize how vaccine safety and effectiveness impact acceptance of a vaccine, and whether this impact varied over time or across socioeconomic and demographic groups. Repeated cross-sectional surveys of an opt-in internet sample were conducted in 2020 in the US, mainland China, Taiwan, Malaysia, Indonesia, and India. Individuals were randomized into receiving information about a hypothetical COVID-19 vaccine with different safety and effectiveness profiles (risk of fever 5% vs. 20% and vaccine effectiveness 50% vs. 95%). We examined the effect of the vaccine profile on vaccine acceptance in a logistic regression model, and included interaction terms between vaccine profile and socioeconomic/demographic variables to examine the differences in sensitivity to the vaccine profile. In total, 12,915 participants were enrolled in the six-country study, including the US (4054), China (2797), Taiwan (1278), Malaysia (1497), Indonesia (1527), and India (1762). Across time and countries, respondents had stronger preferences for a safer and more effective vaccine. For example, in the US in November 2020, acceptance was 3.10 times higher for a 95% effective vaccine with a 5% risk of fever, vs a vaccine 50% effective, with a 20% risk of fever (95% CI: 2.07, 4.63). Across all countries, there was an increase in the effect of the vaccine profile over time (p < 0.0001), with stronger preferences for a more effective and safer vaccine in November 2020 compared to August 2020. Sensitivity to the vaccine profile was also stronger in August compared to November 2020, in younger age groups, among those with lower income; and in those that are vaccine hesitant. Uptake of COVID-19 vaccines could vary in a country based upon effectiveness and availability. Effective communication tools will need to be developed for certain sensitive groups, including young adults, those with lower income, and those more vaccine hesitant.