The complex eukaryotic chaperonin TRiC/CCT helps maintain cellular protein homeostasis, however, its assembly mechanism remains largely unknown. To address the subunit specificity in TRiC assembly, we express each of the individual yeast TRiC subunit in E. coli. Our cryo-EM structural study and biochemical analyses demonstrate that CCT1/2/6 can form TRiC-like homo-oligomeric double ring (HR) complex, however ATP-hydrolysis cannot trigger their ring closure; after deletion of the long N-terminal extension, CCT5 can form the closed double-ring structure; while CCT3/4/7/8 cannot form the HRs. It appears that CCT1 forms a HR in a unique spiral configuration, and ATP-hydrolysis can drive it to re-assemble with an inserted extra subunit-pair. Our data suggest that CCT5 could be the leading subunit in ATP-hydrolysis-driven TRiC ring closure. Moreover, we demonstrate that ADP is sufficient to trigger the assembly of the HRs and TRiC from the assembly intermediate micro-complex form. Our study reveals that through evolution, the more ancestral subunits may have evolved to take more responsibilities in TRiC ring assembly, and we propose a possible assembly mechanism of TRiC involving subunit-pair insertion. Collectively, our study gives hints on the structural basis of subunit specificity in TRiC assembly and cooperativity, beneficial for future TRiC-related therapeutic strategy development.