In order to analyze the productivity of the multi-branched horizontal wells in the coalbed methane（CBM）reservoir，a productivity model for multi-branched horizontal wells in a CBM reservoir is proposed，which considers stress sensitivity in the cleat system and the unsteady diffusion in the matrix system based on the basic theory of the fluid flow mechanism through porous media. The mathematical model is solved through the methods of the point source function，Pedrosa transformation，Perturbation transformation，Laplace transformation，Finite cosine transformation，Element discretization，and Superposition principle. The typical production decline curve is plotted by Stehfest numerical inversion，which is divided into nine different flow regimes according to the characteristics of this curve. Also，the model validation and the comparison of the pseudo-steady diffusion and unsteady diffusion are conducted. Then sensitivity parameter analysis is carried out，such as the permeability modulus，length of branches and number of branches. We summarized the effect of different parameters on production performance. The related research enriches the studies of the production performance of multibranched horizontal wells in a CBM reservoir and provides certain theoretical guidance for the development of a CBM reservoir.