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We developed a detailed Monte Carlo simulation method to study the time resolution of detectors for time-of-flight positron emission tomography (TOF PET). The process of gamma ray interaction in detectors, scintillation light emission and transport inside the detectors, the photoelectron generation and anode signal generation in the photomultiplier tube (PMT), and the electronics process of discriminator are simulated. We tested this simulation method using published experimental data, and found that it can generate reliable results. Using this method, we simulated the time resolution for a 13 times 13 detector block of 4 times 4 times 20 mm3 lutetium orthosilicate (LSO) crystals coupled to four 2-inch PMTs using PMT-quadrant-sharing (PQS) technology. We analyzed the effects of several factors, including the number of photoelectrons, light transport, transit time spread (TTS), and the depth of interaction (DOI). The simulation results indicated that system time resolution of 360 ps should be possible with currently available fast PMTs. This simulation method can also be used to simulate the time resolution of other detector design method.