Most existing individual accessibility studies ignore travel time uncertainties commonly encountered in congested road networks. This study investigates the impacts of travel time uncertainties on the equity of individual accessibility using spatiotemporal big data collected in Shenzhen, China. The collected big data are utilized to extract travel time distribution information and mobility data of a large number of individual samples across the entire study area. Two reliability-based individual accessibility measures are proposed to evaluate individual accessibility by explicitly considering the individual's reliability constraint in the activity-travel scheduling. The proposed measures are further applied to quantify the travel time uncertainty impacts on individual accessibility to healthy food retailers in Shenzhen. Results of this study suggest that travel time uncertainties have distinct impacts of travel time uncertainties on accessibility of different people groups; and underscore that traditional accessibility measures ignoring travel time uncertainties can lead to significant bias on the evaluation of individual accessibility and associated equity issues.