Bubble lodgment in complex capillary network is a common issue in many industrial and biological processes. Research work reported in literature only investigated bubble dislodgement in single channels, and did not consider the effect of network complexity on the dislodgement. This paper focuses on the pressure required to dislodge single bubble from a microscopic capillary network, and investigates what factors affecting the dislodging pressure, to facilitate the precise control of bubble flows in porous media. A capillary network with multi-bifurcation and smoothly-changed diameter is designed to closely mimic the structure of the physiological vascular networks. Over 600 bubble dislodgement experiments have been conducted to understand the effect of network structure, channel dimensions, and bubble length on the dislodging pressure. The results indicate that network structure is a dominant factor affecting the dislodging pressure, and dislodging pressure increases with the increase in network complexity. The effect of bubble length on the dislodging pressure depends on bubble length. When the bubble length is less than a certain value, which is around 2 mm in this study, the dislodging pressure increases significantly with the decrease of bubble length. Once the bubble length is larger than 2 mm, the dislodging pressure is independent of bubble length. A model has been proposed to explain the bubble dislodgement in complex capillary networks. The impact of network structure on the bubble dislodging pressure is characterized by a parameter cj. The model indicates that the dislodging pressure is the function of bubble length, channel dimension and network structure. The analysis of model parameters and shows that parameter cj, rather than the channel size dominates the dislodging pressure for bubbles with length greater than 2 mm, and the increase rate of the dislodging pressure is significantly affected by both channel size and parameter cj.