The molecular dynamics method, based on an empirical potential energy surface, was used to study the effect of catalyst particle size on the growth mechanism and structure of single-walled carbon nanotubes (SWNTs). The temperature for nanotube nucleation (800-1100 K), which occurs on the surface of the cluster, is similar to that used in catalyst chemical vapor deposition experiments, and the growth mechanism, which is described within the vapor-liquid-solid model, is the same for all cluster sizes studied here (iron clusters containing between 10 and 200 atoms were simulated). Large catalyst particles, which contain at least 20 iron atoms, nucleate SWNTs that have a far better tubular structure than SWNTs nucleated from smaller clusters. In addition, the SWNTs that grow from the larger clusters have diameters that are similar to the cluster diameter, whereas the smaller clusters, which have diameters less than 0.5 nm, nucleate nanotubes that are approximately 0.6-0.7 nm in diameter. This is in agreement with the experimental observations that SWNT diameters are similar to the catalyst particle diameter, and that the narrowest free-standing SWNT is 0.6-0.7 nm.