This paper reports the theoretical and experimental study on a Rb atomic Faraday resonance optical filter (AFROF). Considering Rb atomic hyperfine Zeeman splittings, we analysed theoretically the transmission performance of Rb-AFROF. The changes of the operation frequency and bandwidth of Rb-AFROF with magnetic fields and temperature are observed. The results show that the bandwidth is smaller than 3 GHz, ths transmission efficiency -50%, the minimum detected light power -0.1μW.