The improvement of time resolution in time-of-flight positron emission tomography (TOF-PET) relies on the development of scintillation materials and photodetectors. With the introduction of Cherenkov TOF-PET, higher requirements have been placed on the intrinsic timing performance of photodetectors. Our team has proposed a Cherenkov Radiator Window Photomultiplier tube (CRW-FPMT) that uses the Cherenkov radiator directly as the light window, which eliminates the boundary between the scintillator and the photodetector for fast time resolution. This paper mainly discusses the factors influencing its time resolution and optimizes it to achieve a single photon time resolution of 27.2 ps.