A model for partial discharge (PD) propagation in a single channel of an electrical tree is proposed. PD is induced by the high field near the needle tip, then propagates along the channel by field enhancement due to charge injection by PD, and stops propagating when the field becomes less than a certain value due to field divergence. This model suggests that the field distribution and the tree growth process are closely related to the behavior of PD. By considering the influences of gas pressure and the applied-voltage frequency on the behavior of PD, various phenomena of tree growth, such as the bush formation under higher gas pressure and low frequency, are qualitatively explained. This model also suggests a relation between PD and the fractal nature of treeing breakdown.