Oral respiration causes constriction of the upper airway in the retropalatal and retroglossal regions, thereby increasing the risk of sleep disorder. One of the best methods to detect early signs of obstructive sleep apnea syndrome (OSAS) is daily monitoring of the respiration rate and mode of respiration during sleep. The vital signs are measured by a noncontact method in order to avoid burdening the subject and to allow differentiation between the various respiratory modes. In this study, we developed a system to measure the respiration rate and mode using far- and near-infrared cameras, and assessed the effectiveness of the proposed system and algorithm. A near-infrared camera detected the positions of the nostril and mouth, which are the pathways of expired and inspired air, respectively; while the far-infrared camera measured temperature changes in the nostril and mouth to derive the respiration rate and mode for detecting apnea. We enrolled 10 participants and measured their respiration rates using the aforementioned system under three states: nasal respiration, oral respiration, and apnea. The root-mean-square error for the respiration rate was 0.27 bpm, indicating that the system measured respiration without error in 92% of the trials. There was no error in discriminating between nasal and oral respiration. Additionally, this system detected apnea quite satisfactorily. The results of the experiment confirm that the system we developed effectively measures respiration in a noncontact manner.