Coal bed methane (CBM) significantly contributes to unconventional energy resources. With the development of the drilling technology, multi-branched horizontal wells (MBHWs) have been put into the exploitation of CBM. In this paper, a semi-analytical mathematical model is introduced to study the production characteristics of MBHWs in the composite CBM reservoir. Stress sensitivity, composite reservoir, and complex seepage mechanisms (desorption, diffusion, and Darcy flow) are taken into consideration. Through Pedrosa transformation, Perturbation transformation, Laplace transformation, Finite cosine transformation, element discretization, superposition principle, and Stehfest numerical inversion, pseudo-pressure dynamic curves and production decline curves are plotted and 13 flow regimes are divided. Then, the sensitivity analysis of related parameters is conducted to study the influences of these parameters based on these two type curves. Model verification and field application are introduced which shows that the model is reliable. The model proposed in this paper and relevant results analysis can provide some significant guidance for a better understanding of the production behavior of MBHWs in the composite CBM reservoir.