We demonstrate a narrowband optical filter which operates on the 52S1/2 to 52P3/2 transition at 780 nm in rubidium vapor based on optical-pumping-induced dichroism combined with Faraday anomalous dispersion effects. Its peak transmission is 18.4(2)% at the 52S1/2, F = 2 to 52P3/2, F ' = 1, 3 crossover transition, whereas at the 52S1/2, F = 2 to 52P3/2, F ' = 2, 3 crossover transition the transmission is 18.6(2)%. Both transitions have a bandwidth (full-width at half-maximum of peak transmission) as narrow as 24.5(8) MHz, which is remarkably improved compared with the narrowest bandwidth as we know. This technique can also be applied to other alkali atoms.