A carbon nanotube film structure includes at least two overlapped carbon nanotube films, with adjoining films being aligned in different directions. Each carbon nanotube film includes a plurality of successive carbon nanotube bundles aligned in the same direction. The carbon nanotube structure further includes a plurality of micropores formed by/between the adjoining carbon nanotube bundles. A method for fabricating the carbon nanotube film structure includes the steps of: (a) providing an array of carbon nanotubes; (b) pulling out, using a tool, one carbon nanotube film from the array of carbon nanotubes; (c) providing a frame and adhering the carbon nanotube film to the frame; (d) repeating steps (b) and (c), depositing each successive film on a preceding film, thereby achieving at least a two-layer carbon nanotube film; and (e) peeling the carbon nanotube film off the frame to achieve the carbon nanotube structure.