Sesame (Sesamum indicum L.) is one of the oldest oil crops and is widely cultivated in Asia and Africa. The aim of this study was to assess the genetic diversity, phylogenetic relationships and population structure of 277 sesame core collection accessions collected from 15 countries in four different continents. A total of 158 alleles were detected among the sesame accessions, with the number varying from 3 to 25 alleles per locus and an average of 11.3. Polymorphism information content values ranged from 0.34 to 0.84, with an average of 0.568. These values indicated a high genetic diversity at 14 loci both among and within the populations. Of these, 44 genotype-specific alleles were identified in 12 of the 14 polymorphic simple sequence repeat markers. The core collection preserved a much higher level of genetic variation. Therefore, 10.1% was selected as the best sampling percentage from the whole collection when constructing the core collection. The 277 core collection accessions formed four robust clusters in the unweighted pair group method and the arithmetic averages (UPGMA) dendrogram, although the clustering did not indicate any clear division among the sesame accessions based on their geographical locations. Similar patterns were obtained using model-based structure analysis and country-based dendrograms, as some accessions situated geographically far apart were grouped together in the same cluster. The results of these analyses will increase our understanding of the genotype-specific alleles, genetic diversity and population structure of core collections, and the information can be used for the development of a future breeding strategy to improve sesame yield.