Automatic respiration monitoring of dairy cows in modern farming not only helps to reduce manual labor but also increases the automation of health assessment. It is common for cows to congregate on farms, which poses a challenge for manual observation of cow status because they physically occlude each other. In this study, we propose a method that can monitor the respiratory behavior of multiple cows. Initially, 4,000 manually labeled images were used to fine-tune the YOLACT (You Only Look At CoefficienTs) model for recognition and segmentation of multiple cows. Respiratory behavior in the resting state could better reflect their health status. Then, the specific resting states (lying resting, standing resting) of different cows were identified by fusing the convolutional neural network and bidirectional long and short-term memory algorithms. Finally, the corresponding detection algorithms (lying and standing resting) were used for respiratory behavior monitoring. The test results of 60 videos containing different interference factors indicated that the accuracy of respiratory behavior monitoring of multiple cows in 54 videos was >90.00%, and that of 4 videos was 100.00%. The average accuracy of the proposed method was 93.56%, and the mean absolute error and root mean square error were 3.42 and 3.74, respectively. Furthermore, the effectiveness of the method was analyzed for simultaneous monitoring of respiratory behavior of multiple cows under movement, occlusion disturbance, and behavioral changes. It was feasible to monitor the respiratory behavior of multiple cows based on the proposed algorithm. This study could provide an a priori technical basis for respiratory behavior monitoring and automatic diagnosis of respiratory-related diseases of multiple dairy cows based on biomedical engineering technology. In addition, it may stimulate researchers to develop robots with health-sensing functions that are oriented toward precision livestock farming.