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