Positron Emission Tomography (PET) using time-of-flight information, which can greatly improve the quality of the reconstructed image, has recently become an exciting topic. In this work, 3.2mm*3.2mm*25mm finger-like LYSO crystals were used to make a 5*5 array, coupled to the Hamamatsu H8500 photomultiplier tube (PMT) as a detector. A fast leading-edge discriminator was designed for the LYSO-H8500 detector. Average coincidence time resolution FWHM of 330 ps was obtained for the LYSO detector with a reference BaF2 detector, whose time resolution for 511 keV {\gamma}-rays was FWHM 150 ps. Time resolution FWHM of 294 ps was calculated for the LYSO detector, and coincidence time resolution of FHWM 415 ps can be expected for two identical LYSO detectors.
