In this article, the diameter distributions of carbon nanotube were theoretically analyzed. The carbon nanotubes were grown by microwave plasma enhanced CVD. For studying the diameter distributions of the carbon nanotubes, the thermodynamic transformation of catalytic films was theoretically considered. Therefore, a process of the formation of stable catalytic islands was supposed, in which the initial continuous catalytic films were first transformed into many critical nuclei and then became stable islands through diffusion of the critical particles, where carbon nanotubes just grew up. The island distribution expression can be derived, and under certain conditions, carbon nanotubes have similar distributions. The nanotubes grown on different catalyst films were analyzed, which showed that the nanotubes over thick films have broad diameter distributions and large mean diameters, while that over thin films have narrow diameter ranges and small diameters on average. The theoretical results were in good agreement with the experimental data.