Pulse shape, dark counts, photon-detection efficiency, cross talks were identified as critical factors affecting timing resolution after an extensive measurement of solid-state photomultipliers (SSPM) for time-of-flight PET. Among those factors, pulse shape has been investigated through a SPICE simulation, and the measurement of single photoelectron and 511keV gamma ray pulses. First, we showed that, due to the long recovery tail in a single photon pulse, the risetime of 511keV gamma ray pulse from LYSO/MPPC is much slower than the one of PMT. Second, we showed that the parasitic quenching capacitance of the quenching resistor could play an important role in supplying a quick charge in the avalanche process and improve the single photon pulse shape. Third, by changing the parasitic quenching capacitance, we showed that it could be used to improve the risetime of 511keV gamma ray pulse that is directly related to the timing performance of SSPM.