This paper proposes a reliability analysis framework for glass fiber-reinforced polymer- (GFRP-) reinforced concrete systems with uncertain capacities and demands over time. Unfortunately, there has been limited discussion or research done related to the potential change of failure modes over time. Therefore, a rational approach is needed to integrate multiple failure modes in a single analysis framework, considering uncertainties of time-variant demands and capacities. To account for multiple failure modes, this study proposes the limit state function to estimate the safety margin, based on strain values of GFRP-reinforcing bars. A proposed limit state function can capture the likelihood of both shear and flexural failure modes, simultaneously. In this study, seven typical bridge deck configurations (e.g., varied deck thickness, girder spacing, and bar size) were exposed to various ambient temperatures. Simulation results show that reliability indices of 100-year exposure exhibit significant variance, ranging from 2.35 to 0.93, with exposure temperatures ranging from 13 to 33°C. Exposure temperature and time are the dominant factors influencing the reliability indices, so are the ones that need to be changed. As exposure time and/or exposure temperature increase, the flexural capacity model plays an important role to determine the reliability indices. When flexural and shear failure modes are equally dominant, reliability indices can capture risks of both failures, using the proposed strain-based approach.