How to quantitatively evaluate the permeability change of coalbed subjected to liquid nitrogen cooling is a key issue of enhanced-permeability technology of coalbed. To analyze the evolution process of permeability of coupled coal deformation, failure and liquid introgen cooling, the coal is supposed as elastic, brittle and plastic material. Its deformation process includes elastic deformation stage, brittle strength degradation stage and residual plastic flow stage. Combined with strength degradation index, dilatancy index of the element and Mohr-Column strength criterion, the element scale constitutive model with the effects of confining pressure on peak-post mechanical behaviors is built. Based on the deformation process of coal rock, there exist two stages of permeability evolution of the element including decrease of permeability due to elastic contraction and increase due to coal rock element's failure. The relationships between the permeability and elastic deformation, shear failure and tension failure for coal are studied. The permeability will be influenced by the change of pore space due to elastic contraction or tension of element. Conjugate shear zones appear during the shear failure of the element, in which the flow follows so-called cubic law between smooth parallel plates. The calculation formulas of the permeability and the aperture of the fractures are given out based on the volumetric strain. When tension failure criterion is satisfied with the rock element fails and two orthogonal fractures appear. The calculation formulas of the permeability and the width of the fractures are given out based on the volumetric strain. Further, combined with the thermal conduction theory the permeability evolution model of coupled coal deformation, failure and liquid nitrogen cooling is presented. Then Fish function method in FLAC is employed to perform the model. The permeability's evolution process for coal bed cryogenically stimulated by flowing liquid nitrogen through gas production well in Wangyingzi mine, Liaoning province, is simulated and the results include: 1) When liquid nitrogen(LN2) is injected into a rock at warm reservoir temperature, heat from the rock will quickly transfer to the liquid nitrogen resulting in rapid cooling and contraction of coal bed. The nearer the position is to bore hole, the bigger the shrinkage deformation and thermal stress and coal fail when tension stress sufficiently built up. In this paper the tension failure band after 10 days' LN2 cooling is 0.65 m. 2) In tension failure area the cracks from cooling stimulation lead to the significant growth of permeability. The maximum permeability for element is 1.97×105 times more than that before cooling. 3) Apart from the bore hole, the thermal tensile stress leads to the growth of permeability at a rate of 1%~14%, far less than that in the tension failure area. 4) With increasing time the failure area gradually slowly grows up. It indicates that the longer cooling time does not mean better effects. 5) The cooling fracturing area is found to have a 1.0 m band. In practical engineering the pressure in hole bore and phase transition of water also influences the deformation and failure of coal, which leads to much more failure zone of cooling. 6) The evolution process of permeability of coupled coal deformation, failure and liquid introgen cooling can be better reflected by the model in this paper. This study is hoped to provide a simple but reasonable description of the permeability evolution of rocks subject to liquid nitrogen cooling.