The finite volume method (FVM) can adapt to complex boundaries, achieve conservation of integrals, and generate flexible integral grids. Compared with the finite difference method (FDM), the FVM is immune to numerical oscillations and numerical dispersions. This paper aims to simulate the coalbed methane (CBM)-water two-phase flow in complex coal rock, and predict the CBM and water outputs in an accurate manner. Therefore, the FVM was introduced to create a simulation model of coalbed methane (CBM) productivity in 3D dual-porosity coal reservoir under non-equilibrium adsorption and pseudo-steady state conditions. The established model was applied to an actual project in Qinshui Basin, Shanxi Province, China. The historical gas and water outputs of a single CBM well were fitted with our model, and the simulated curves agree with the overall trend of the historical drainage and production curves. Next, the change trends of gas and water outputs in the CBM well were predicted, and the sensitivities of gas well productivity to three main reservoir parameters were analyzed. The results correctly reflect the productivity trend of the CBM well, indicating the correctness and feasibility of our model. Our research effectively simulates the migration of the CBM in coal rock with complex boundaries, providing a valuable reference for the development of the CBM.