Polyacrylonitrile (PAN)/$Fe_2O_3$ nanocomposite membranes with a thickness of 0.02 mm were electrospun by adding 0 to 5 wt% of $Fe_2O_3$ into PAN. The surface tension, density, kinematic viscosity and dynamic viscosity of the PAN solution were determined to be $33.8{pm}1mN/m$, 0.9794 g/ml, $1548.6mm^2/sec$ and 1516.7 cP, respectively. The average diameters of PAN fibers containing 0, 1 2, 3, and 4 wt% $Fe_2O_3$ particles were 300, 260, 210, 130, and 90 nm, respectively. Fourier-transform infrared spectroscopy results showed that the addition of $Fe_2O_3$ nanoparticles to the PAN mat reduced the absorption peak intensity at $2242cm^{-1}$ ($C{equiv}N$ bond) while it caused a sharp increase in the peak intensity at $2356cm^{-1}$(C=O bond). Thus, it appears that an appropriate amount of $Fe_2O_3$ nanoparticles in the PAN backbone leads to an improvement of the performance of the $CO_2$ gas sensor, most likely due to the change of functional groups in the membrane.