Chemical detection of toxic gases, such as greenhouse gases is still very important as a research topic. To design gas sensor detectors based on single-walled carbon nanotubes (SWCNTs) with high sensitivity and selectivity for the toxic environment is a continuous process. The aim is to detect NO$_2$ gas with better sensitivity. In the present work, the thin-film sensor is fabricated on SiO$_2$ substrate and it is functionalized with polyethylenimine (PEI). It has been established that PEI functionalized SWCNTs (F-SWCNTs) show high sensitivity towards strong electron-withdrawing particles. It was found that at room temperature, SWCNTs-PEI functionalized gas sensor exhibited a higher sensitivity of 37.00% as compared with bare SWCNTs gas sensor. The gas sensor has shown the repeatable response for the entire concentration range studied.The sensing properties and the PEI functionalization duration effects on the behaviour of SWCNTs-based gas sensors were demonstrated.