We demonstrate highly sensitive and selective gas sensors based on solution-processed single-wall carbon nanotube (SWCNT) random networks for the detection of nitric oxide (NO) down to the ppb-level operating at room temperature. The proposed gas sensors exhibited a response of 50% under both inert and air atmospheres with a theoretical detection limit of 0.2 ppb and a selectivity toward different target gases of volatile organic compounds, including benzene, toluene, and ammonia. The outstanding sensing performance was realized by functionalizing SWCNT random networks with polyethylenimine (PEI), which possesses a repeating structure of amine groups. We investigate the functionalization properties of SWCNT random networks by using atomic force microscopy, X-ray photoelectron spectroscopy and Raman spectroscopy and the sensing mechanism in the proposed NO gas sensors. We note that solution-process technologies, from the deposition of SWCNT random networks to the polymeric functionalization of amine groups, were employed at room temperature under an ambient atmosphere to fabricate highly sensitive and selective NO gas sensors, which are based on low-cost, effective, and scalable merits in the industry of sensors. We also investigate the effect of ultraviolet (UV) irradiation on the recovery time underlying the sensing mechanism. Photodesorption energy obtained by UV irradiation reduced the recovery time of the proposed NO gas sensors to within a few tens of seconds. We believe that this work is a promising and practical approach for realizing health-care monitoring systems by real-time analyzing NO gas at the ppb level in the field of biosensors.