CoalBed Methane (CBM), as one kind of unconventional gas, is an important energy resource, attracting industry interest in research and development. Using the Langmuir adsorption isotherm, Fick’s law in the matrix and Darcy flow in cleat fractures, and treating the Stimulated Reservoir Volume (SRV) induced by hydraulic fracturing as a radial composite model, the continuous linear source function with constant production is derived by the methods of the Laplace transform and Duhamel theory. Based on the linear source function, semi-analytical solutions are obtained for a fractured vertical well producing at a constant production rate or constant bottom-hole pressure. With the help of the Stehfest numerical algorithm and computer programing, the well test and rate decline type curves are obtained, and the key flow regimes of fractured CBM wells are: wellbore storage, linear flow in SRV region, diffusion flow and later pseudo-radial flow. Finally, we analyze the effect of various parameters, such as the Langmuir volume, radius and permeability in the SRV region, on the production performance. The research results concluded in this paper have significant importance in terms of the development, well test interpretations and production performance analysis of unconventional gas.