An open-close member control apparatus is to prevent a foreign matter from being trapped to a window glass serving as an open-close member that is driven to open by manipulation of a manipulation switch. When a trapping detection section determines that the foreign matter is trapped to the window glass, power supply to a driving device is stopped to stop opening of the window glass. Then, it is determined whether a predetermined condition is satisfied for approving re-open of the window glass. When the predetermined condition is satisfied, the power supply to the driving device is re-started. Opening of the window glass is thereby enabled again.