Microfracture structures of coal seams are the key parameters in the context of enhanced coalbed methane (ECBM) recovery as they determine permeability and productivity. Significant progress has been made in fracture characteristics, however, the detailed structural and fractal characteristics of microfractures of different rank coals (especially high-rank coals in China) are poorly understood. This study aims to analyze the physical characteristics of microfractures with X-ray computed tomography (X-ray CT) and fractal theory, identify the effects of coal rank on the physical properties of microfractures, and discern the relationship between fractal features and permeability. The results show that the experimental coals are dominated by type B microfractures, followed by type A microfractures. Additionally, for the coals investigated in this study, the microfracture network in low-rank coals is usually well-connective, whereas the connectivity and scale of the microfracture network reduces with increasing coal rank. The average microfracture length, width and volume reduces but quantity increases as coal rank increases, and these downward trends can be divided into three stages: rapid decline stage (0.59% < Ro, ran < 1.25%), slow decline stage (1.25% < Ro, ran < 2.25%), and stable stage (Ro, ran > 2.25%). The average aperture first decreases but then slightly increases with coalification. Furthermore, the fractal dimension (D) of these microfractures increases as coal rank increases in the range of 1.64-1.78, indicating that the microfracture structure gets more complicated with coalification. The CT porosity displays a ` U-shaped' trend as the fractal dimension increases: first decreases from 2.12% to 0.94% and then increases from 0.94% to 1.49% (turning point at D= 1.72). These Chinese coal samples have very low to medium permeability, with highly variable values ranging from 0.004 to 1.465 mD. Coals with higher fractal dimensions are commonly less permeable for gas, and such a relationship is especially apparent for coals with higher ranks. The negative correlation between permeability and fractal dimensions means that coals with higher fractal dimensions are not favorable for CBM exploitation. Our results show that microfracture structures contribute to the permeability of coal reservoirs, and that fractal dimensions plays a significant role in assessing the exploitation potential of a coal seam.