Eating a diet rich in vegetables, including green bell peppers, reduces your risk of certain chronic illnesses. The antioxidants in vegetables reduce free radical damage. Free radicals are compounds that cause cell damage that can lead to inflammation, heart problems and cancer. While red bell peppers contain larger amounts of antioxidants, green bell peppers are a significant source as well. Green bell peppers also contain zeaxanthin, which keeps your eyes healthy and might reduce your risk of age-related eye disorders.