Five groups of middle to high rank coal samples (R-o, (max) value between 1.87 and 3.01%) were tested under different confine pressures using nuclear magnetic resonance (NMR) technology. Stress sensitivities of adsorption pore, seepage pore and fracture were calculated to investigate the relationship between the compressibility of pore-fracture system and its effective stress. The heterogeneous variation of pore and fracture caused by the effect of stress was discussed based on the T-2 spectrum by using the NMR method. The conclusions are as follows. 1) The overall compressibility (OC) of the middle rank coal samples is mainly controlled by seepage pore and fracture. Adsorption pore are generally well developed in high-rank coal samples and the pores are primarily responsible for the stress sensitivity of these kinds of samples. 2) The compressibility shows a trend of decrease with increase of coal rank and there exists a good logarithmic relationship between OC and effective stress. 3) With the decrease of OC, the pore and fracture heterogeneity tends to become more complex. The variation of the heterogeneity of middle rank coal sample is higher than that of a high rank coal sample, and the heterogeneity variation of adsorption pore is greater than that of seepage pore and fracture. 4) The effect of stress on the heterogeneity of pore-fracture system has a two-stage characteristic. At the initial stage that the confine pressure is less than 9 MPa, the heterogeneity of pore-fracture system becomes more complicated. And when the stress is higher than 9 MPa, it moves to the stable stage that the heterogeneity tends to be stable. 5) Compared to the middle rank coal samples, the OC of high rank coal reveals a significant negative linear correlation with the (total fractal dimension) D-R, indicating the simultaneity of pore structure and strain variation under the action of stress. The above results can provide theoretical guidance for increased understanding of the changes in a coal reservoir's permeability during coalbed methane drainage.