A pilot numerical model of the Geminid meteoroid stream is presented. This model implies cometary origin of the stream. Ejection of relatively small amount of particles (90 000 test meteoroids with masses 0.02, 0.003 and 0.0003 g) from the asteroid (3200) Phaethon (the parent body) was simulated, and their evolution was followed till the present time. The particles close to the Earth orbit were considered as the `shower'. It was found that the width of the model shower is at least twice less comparatively the real shower. The maximum activity of the model shower is dislocated and occurs about one day late. The most probable reason for both discrepancies is the drastic transformation of the parent body orbit during rapid release of the volatiles in the process of the stream initial formation. The dispersion of the model stream was evaluated in terms of the Southworth-Hawkins D-criterion.