Here we report the observation of the carbon nanotube dendrites, in which a carbon nanotube grows up from the outer wall of another one, in the catalytic pyrolytic product of ferrocene. A simple dendrite consists of two nanotubes directly connected with each other, without any foreign particles between them. The dendritic structure is formed due to the continuous feeding of catalyst particles during the nanotube growth process, and the growth model is proposed. Carbon nanotube dendrites are promising candidates of building blocks in nanoscale electronic devices.