Respiratory diseases including apnea are often accompanied by abnormal respiratory depth, frequency, and rhythm. If different abnormal respiratory patterns can be detected and recorded, with their depth, frequency, and rhythm analyzed, the detection and diagnosis of respiratory diseases can be achieved. High-frequency millimeter-wave radar (76–81 GHz) has low environmental impact, high accuracy, and small volume, which is more suitable for respiratory signal detection and recognition compared with other contact equipment. In this paper, the experimental platform of frequency-modulated continuous wave (FMCW) radar was built at first, realizing the noncontact measurement of vital signs. Secondly, the energy intensity and threshold of respiration signal during each period were calculated by using the rectangular window, and the accurate judgment of apnea was realized via numerical comparison. Thirdly, the features of respiratory and heart rate signals, the number of peaks and valleys, the difference between peaks and valleys, the average and the standard deviation of normalized short-term energy, and the average and the standard deviation and the minimum of instantaneous frequency, were extracted and analyzed. Finally, support vector machine (SVM) and K-nearest neighbor (KNN) were used to classify the extracted features, and the accuracy was 98.25% and 88.75%, respectively. The classification and recognition of respiratory patterns have been successfully realized.