Abstract: An improved discharge model with a multi-branch streamer pattern was established by considering the carrier density fluctuation based on the Poisson equation and current continuity equation. The discharge results under 120kV, 160kV, and 200kV positive impulse voltage are obtained by COMSOL software, respectively. Results show that the streamer branch pattern of the improved model is closer to the experimental discharge phenomenon than the original model. The maximum field strength is mainly distributed in the streamer head, and all exceed 2×10⁸ V/m, and the field strength and charge changes caused by the secondary streamer at 200 kV are the most obvious. In addition, the propagation length and velocity of the z-axis streamer under three voltages also show that the mutual repulsion of the charges between the streamer branches has a significant effect on the suppression of the propagation of the streamer. Compared with the streamer pattern when the voltage rising time is 5ns, 10ns, 50ns and 120ns: the shorter the voltage rising time, the larger the streamer radius, and the more the branches. This study is helpful to analyze the effect mechanism of carrier density fluctuations on streamer branches during the discharge.