Using solid nanoparticles (NPs) as catalysts is the most effective method to achieve catalytic growth of single-walled carbon nanotubes (SWCNTs) with ultrapure chirality. Until now, SWCNTs with a suitable chirality purity have not been prepared in experiments. That is, the evolution of solid NPs during the catalytic growth of SWCNTs is in contradiction with the original concept of a changeless structure. Hence, in this work, the evolution mechanism of solid cobalt NPs during the nucleation process of SWCNTs is analyzed through molecular dynamics. Similar to the experimental observations, the results show that a drastic structural fluctuation of the NPs occurs during the nucleation of SWCNTs. This structural fluctuation is caused by the fact that the elastic strain energy and surface energy of the NPs can be tuned when a carbon gradient exists between the subsurface and interior of the NP. Furthermore, such a carbon gradient can be reduced by changing the carbon feeding rate. This work not only reveals the evolution mechanism of solid catalysts during the nucleation of SWCNTs but also provides prospects for realizing solid catalysts with a changeless structure by tuning the experimental parameters.