Poly(methyl methacrylate) (PMMA) is widely used in the preservation and exhibition of cultural relics in museums. Accurately predicting its service life can help avoid many negative effects caused by PMMA aging. To study the change in the yellowing index of PMMA after aging in a UV light environment, an aging experiment was conducted. A prediction model for the service life of PMMA was established using nonlinear curve fitting and a back propagation (BP) neural network. By comparing the goodness of fit, simulation and modeling capabilities of the initial data, and the predictive ability for new data, it was found that the BP neural network prediction model outperformed the nonlinear curve fitting prediction model. In this study, the service life of newly produced PMMA samples was calculated as 7.83, 8.47, and 8.42 years, based on the yellowing index of retired PMMA as a benchmark and using the output data from the BP neural network prediction model. At this time, the performance and exhibition effect of the PMMA are poor, and the batch of PMMA needs to be updated.