Synchrotron radiation micro-computed tomography (SR-mu CT) is a critical technique for quantitative characterizing the 3D internal structure of samples, recently the dynamic SR-mu CT has been attracting vast attention since it can evaluate the three-dimensional structure evolution of a sample. A dynamic mu CT method, which is based on monochromatic beam, was developed at the X-ray Imaging and Biomedical Application Beamline at Shanghai Synchrotron Radiation Facility, by combining the compressed sensing based CT reconstruction algorithm and hardware upgrade. The monochromatic beam based method can achieve quantitative information, and lower dose than the white beam base method in which the lower energy beam is absorbed by the sample rather than contribute to the final imaging signal. The developed method is successfully used to investigate the compression of the air sac during respiration in a bell cricket, providing new knowledge for further research on the insect respiratory system.