This study presents the development and application of a fully coupled two-phase (methane and water) flow, transport, and poromechanics numerical model for the analysis of geomechanical impacts on coalbed methane (CBM) production. The model considers changes in two-phase fluid flow properties, i.e., coal porosity, permeability, water retention, and relative permeability curves through changes in cleat fractures induced by effective stress variations and desorption-induced shrinkage. The coupled simulator is first verified for poromechanics coupling, and simulation parameters of a CBM reservoir model are calibrated by history matching against one year of CBM production field data from Shanxi Province, China. Then, the verified simulator and the calibrated CBM reservoir model are used for predicting the impact of geomechanics on the production rate for twenty years of continuous CBM production. The simulation results show that desorption-induced shrinkage is the dominant process in increasing permeability in the near wellbore region. Away from the wellbore, desorption-induced shrinkage is weaker, and permeability is reduced by pressure depletion and increased effective stress. A sensitivity analysis shows that for coal with a higher sorption strain, a larger initial Young's modulus and a smaller Poisson's ratio promote the enhancement of permeability as well as an increased production rate. Moreover, the conceptual model of the cleat system, whether dominated by vertical cleats with permeability correlated to horizontal stress or with permeability correlated to mean stress, can have a significant impact on the predicted production rate. Overall, the study clearly demonstrates and confirms the critical importance of considering geomechanics for an accurate prediction of CBM production.