The retina is highly susceptible to the generation of toxic reactive oxygen species (ROS) that disrupt the normal operations of retinal cells. The glutathione (GSH) antioxidant system plays an important role in mitigating ROS. To perform its protective functions, GSH depends on nicotinamide adenine dinucleotide phosphate (NADPH) produced through the pentose phosphate pathway. This work develops the first mathematical model for the GSH antioxidant system in the outer retina, capturing the most essential components for formation of ROS, GSH production, its oxidation in detoxifying ROS, and subsequent reduction by NADPH. We calibrate and validate the model using experimental measurements, at different postnatal days up to PN28, from control mice and from the rd1 mouse model for the disease retinitis pigmentosa (RP). Global sensitivity analysis is then applied to examine the model behavior and identify the pathways with the greatest impact in control compared to RP conditions. The findings underscore the importance of GSH and NADPH production in dealing with oxidative stress during retinal development, especially after peak rod degeneration occurs in RP, leading to increased oxygen tension. This suggests that stimulation of GSH and NADPH synthesis could be a potential intervention strategy in degenerative mouse retinas with RP.