Information on genetic relationships and pedigree structure in germplasm collections is vital to breeders in crop improvement programs. In this study, we assessed genetic identity, kinship distance, and parentage–sibship relationships among 37 peach (Prunus persica) accessions and breeding lines using simple sequence repeat (SSR) markers. Pairwise comparisons based on multilocus SSR profiles led to the identification of two synonymous groups including five accessions. Two pairs of parent–offspring and one full sibling relationships were identified using the likelihood method, and Bayesian cluster analysis partitioned the accessions into groups that were partially compatible with the known pedigree, origin, and flesh color. The 37 accessions were grouped into four clusters, which were largely supported by the known pedigree and origin of these accessions. Although the observed mean heterozygosity was 0.219, mean inbreeding coefficient was 0.635, indicating a high degree of inbreeding among the accessions. Eleven of the 15 SSR markers (73.3%) tested were transferable to nine related Prunus species. Results of the study demonstrate that these SSRs could facilitate the assessment of genetic identity and pedigree structure.