Flexible and easily-processable materials exhibiting excellent electromagnetic interference (EMI) shielding performance are desirable for EMI shielding applications in electronic devices, which are getting progressively smaller and smarter. This study reports single-walled carbon nanotube (SWCNT)/poly(ethylene-alt-maleic anhydride) (PEMA) composite films with an excellent EMI shielding performance fabricated by a simple bar-coating and doping process. The AuCl3-doped SWCNT/PEMA composite films exhibited an excellent EMI shielding effectiveness (SE) of 96.3 dB at a thickness of 0.031 mm. The EMI SE values of the AuCl3-doped SWCNT/PEMA composite films are higher than any other reported synthetic materials with a similar thickness. The excellent EMI shielding performance is attributed to the high electrical conductivity. The conductivity of the SWCNT/PEMA composite films can be increased effectively to 8500 S cm-1 through the AuCl3-doping process. It was further confirmed by MD simulations that the introduction of only 30 wt.% PEMA polymer is effective for obtaining well-dispersed SWCNTs in the composite films. It is noteworthy that such a small fraction of PEMA polymers is advantageous both for decreasing the volume fraction of the insulating polymers and facilitating the chemisorption of dopants onto the SWCNT surfaces.