Temporal characteristics of photoelectrons emitted by photoelectric cathodes affect the temporal resolution of time analysis instruments such as streak cameras and electron diffraction systems. Energy, angle distribution model and stochastic sampling method of photoelectrons are investigated by Monte Carlo method. The fast multiplicative sampling method is given for the cosine and Maxwell distribution of energy. Time dispersion values of seven energy models of photoelectron, such as cosine, Maxwell, Beta, Rayleigh and Henke distribution, are calculated. The dispersion coefficient of time dispersion formula is verified to be 2.643 kg1/2·A-1·s-1, and the exponential relationship with the accelerated electric field strength is -0.996. The method and results are useful in the fields such as dynamics of femtosecond photoelectron propagation, femtosecond streak cameras, femtosecond electron diffractometer.