To control the length and morphology of carbon nanotubes(CNTs) is difficult in its producing process. Influencing factors of length and morphology of carbon nanotubes have been analyzed in the catalytic chemical vapor deposition (CCVD) process. According to the growth characteristic of carbon nanotubes, the diffusion model was developed. Over time, the diffusion potential decreases due to a reduction in the carbon atom concentration gradient. With the model, the shape of catalytic particle is analyzed. From theoretical derivation, it is demonstrated that with the temperature ranging from 1173K to1373K, the growth rate raises up sharply with the increasing of temperature. Growth rate of CNTs increases with increasing layers at the same temperature.