Permeability of coal seams is one of the key factors for the success of coalbed methane (CBM) developments. It is dominated by cleat permeability in coal, which is very sensitive to the change of effective stresses. The coal matrix shrinkage due to methane production also influences cleat permeability. Using an explicit-coup ling simulation method, which simultaneously simulates multiphase fluid flow and coal deformation, and a coupling permeability model, which considers the effects of the effective stress change and coal matrix shrinkage on cleat permeability, the sensitivity of CBM production to ten engineering, geologic, and coal intrinsic parameters such as cleat permeability, cleat spacing, well control area, depth, and methane content, etc., were studied in this paper. These parameters are stress and matrix shrinkage related parameters or have significantly influences on CBM production identified from previous studies. The production rate and final gas recovery from conventional simulations and coupling simulations are also compared. Of the parameters studied, permeability, cleat spacing, and in situ stresses were found to be the most sensitive parameters that influence CBM production. Medium sensitivity was found for the coefficient of matrix shrinkage, the Langmuir volume, pressure gradient, and well control area, while the least sensitive parameters included Poisson's ratio, Young's modulus, and the Langmuir pressure.