The controlling factor of the CO2 permeance of an ion gel membrane containing a task-specific ionic liquid (tetraphosphonium prolinate) as the CO2 carrier was investigated. Tough double-network (DN) ion gel membranes with different thicknesses were fabricated, and their CO2 permeances were evaluated. The results showed that the CO2 permeance of the DN ion gel membrane was not inversely proportional to the membrane thickness, indicating that the CO2 permeance of the membrane was not controlled by diffusion. A theoretical analysis of the relationship between CO2 permeance and the thickness of the membrane revealed that the CO2 stripping rate at the permeate side greatly affected the CO2 permeance of the DN ion gel membrane. Therefore, increasing the decomposition reaction rate of the CO2–carrier complex would be the most important issue for achieving a high CO2 permeance of ion gel membranes containing a task-specific ionic liquid.