A 780 nm Rb Faraday atomic dispersive optical filter (FADOF) that operates in the wings of Rb D2 resonance line is experimentally studied with a single photon detector. The measure result shows that the maximum transmission of the 780nm Rb FADOF is 28% and the full width at half maximum is 0.7 GHz. A minimum detectable laser power of 0.16 pW/cm2 is obtained with the signal-to-noise ratio of transmission spectrum of 2. Therefore, the detection sensitivity of Rb FADOF is remarkably increased when a single photon detector is used. If the Rb FADOF is used to replace a interferential optical filter in laser communication, it can lead to a lower bit error ratio and the system that operates with single photon detector is able to work during daytime when optical background is much larger.