The Mu2e experiment at Fermilab proposes to search for the coherent neutrino-less conversion of muons to electrons in the presence of a nucleus. The experimental signature for an aluminum target is an isolated 105 MeV electron exiting the stopping target no earlier than ~700 ns after the pulse of proton beam hits the production target. Any protons that hit the production target in between the pulses can lead to fake conversion electrons during the measurement period. We define the beam extinction as the ratio of the number of protons striking the production target between pulses to the number striking the target during the pulses. It has been established that an extinction of approximately 10-10 is required to reduce the backgrounds to an acceptable level. It would be desirable to measure the extinction of the beam coming out of the accelerator in a minute or less. Studies for the fast extinction monitor based on Hamamatsu PMT R7056 is the subject of this presentation.