An AlGaN/GaN multi-shell structure on a GaN nanorod (NR) is formed by using the self-catalytic pulsed growth process of metalorganic chemical vapor deposition with Ga and Al/N supplies in the first and second half-cycles, respectively. With Al supply, a thin AlGaN layer is precipitated near the end of a growth cycle to form the AlGaN/GaN structure. Because of the lower chemical potential for GaN nucleation, when compared with AlN, a GaN layer is first deposited in a growth cycle. AlGaN is not precipitated until the AlN nucleation probability becomes higher when the catalytic Ga droplet is almost exhausted. Because the Al adatoms on the NR sidewalls hinder the upward migration of Ga adatoms for contributing to the Ga droplet at the NR top, the size of the Ga droplet decreases along growth cycle leading to the decrease of GaN layer thickness at the top until a steady state is reached. In this process, the slant facet of an NR changes from the (1-102)-plane into (1-101)-plane. To interpret the observed growth behaviors, formulations are derived for theoretically modeling the AlN nucleation probability, NR height increment in each growth cycle, and the time of exhausting the Ga droplet in a cycle.