Positive underwater discharge can produce abundant physical and chemical effects and is widely used in the fields of energy source exploration and sterilization. However, the physical mechanisms involved in initiation and propagation of streamer are complex and have not been fully revealed, which limit the efficiency of underwater discharge applications. In this paper, we explore the mode-transition, reillumination and branching characteristics of positive filamentary streamer. The influence of deposited charge and space charge distribution on the propagation of streamer channel is clarified. Our research shows that the positive polarity filamentary streamers can be divided into primary streamer and secondary streamer, and the mode transition of discharges is greatly affected by the gas/liquid interface charge relaxation process. When the applied voltage reaches the accelerating voltage, the primary streamer rapidly transits into secondary streamer. The gas/liquid interface charge density and electric field in primary streamer channel are closely related with initiation, termination and reignition of discharge. The space charge distribution of secondary streamer is greatly affected by the voltage rising edge and the electrode surface structure. Longer voltage rise time leads to lower density of space charge and electric field at the head of streamer channel, which causes the decrease of streamer velocity. With larger radius of the micro-convex structure on the electrode surface, the branching of streamer will take place at the root of the main channel instead of electrode surface. Due to the variation of the spatial charge distribution, the velocity of the branching channel shows a trend of first declining and then increasing when the radius of the micro-convex structure is 5 μm.