To reveal the impact of formation and development of the streamer discharge on the dielectric liquid formed between pin-plate electrodes, a numerical model of transformer oil discharge in the electrode system is built which is based on the continuity equations coupled with Poisson’s equation. The influence of applied impulse voltage parameters such as rise time and voltage magnitude on the formation and development of the streamer discharge is evaluated in this model. In addition, the characteristic of the streamer discharge such as streamer velocity, electric field, and radius of streamer head have been investigated. Modeling results reveal that the higher impulse voltage amplitude form streamer discharges with longer paths, thicker columns, higher velocity, and greater radius. In addition, we find that the radius of the streamer head is greatly affected by the percentage of the predetermined electric field tube at the head, and slightly affected when streamer length increased. Modeling results also showed that the rise times had a clear effect on the radius streamer discharge and the distribution of electric fields.