Branch number (BN), vine diameter (VD), longest vine length (VL), petiole length (PL), and internode length (IL) are important agronomic traits that play crucial roles in sweetpotato plant architecture. They are highly correlated with each other and significantly influence storage root yield. An association panel composed of 214 sweetpotato germplasm resources was used to map quantitative trait loci (QTLs) for BN, VD, VL, PL and IL. Through genome-wide association study (GWAS) analysis incorporating data from 3 distinct environments and best linear unbiased estimator (BLUE) values, we identified QTLs with phenotypic variation explained (PVE) ranges as follows: 30 QTLs (9.34–19.58%) for BN; 3 QTLs (10.85–13.82%) for VD; 16 QTLs (9.16–17.58%) for VL; 7 QTLs (9.96–18.01%) for PL; and 26 QTLs (10.31–20.30%) for IL. A total of 8 QTLs (2 of BN, 2 of VL, and 4 of IL) were stably inherited major QTLs, and 7 QTLs were pleiotropic involving BN, VL, PL and IL. Four candidate genes namely itf06g11550.t1, itf09g21940.t1, itf03g15620.t1, and itf06g19990.t1, were identified from 4 stable and major QTLs (qBNnp_5, qVLnp_2, qILnp_4 and qILnp_6) by integrating gene annotation, gene expression analysis and linkage disequilibrium (LD) analysis at SNP sites. The variants in the downstream, exon and intron, and the expression levels of itf06g11550.t1, itf09g21940.t1, and itf06g19990.t1 were significantly correlated with BN, VL and IL respectively. One SNP highly associated with BN developed into a KASP marker, which can be used to assist multi-branch sweetpotato breeding. These results provide a foundation for future gene cloning studies and valuable genetic resources for sweetpotato plant architecture improvement and marker-assisted selection (MAS).