Genetic dissection of yield component traits including kernel characteristics is essential for the continuous improvement in wheat yield. In the present study, one recombinant inbred line (RIL) F6 population derived from a cross between Avocet and Chilero was used to evaluate the phenotypes of kernel traits of thousand-kernel weight (TKW), kernel length (KL), and kernel width (KW) in four environments at three experimental stations during the 2018–2020 wheat growing seasons. The high-density genetic linkage map was constructed with the diversity arrays technology (DArT) markers and the inclusive composite interval mapping (ICIM) method to identify the quantitative trait loci (QTLs) for TKW, KL, and KW. A total of 48 QTLs for three traits were identified in the RIL population on the 21 chromosomes besides 2A, 4D, and 5B, accounting for 3.00%–33.85% of the phenotypic variances. Based on the physical positions of each QTL, nine stable QTL clusters were identified in the RILs, and among these QTL clusters, TaTKW-1A was tightly linked to the DArT marker interval 3950546–1213099, explaining 10.31%–33.85% of the phenotypic variances. A total of 347 high-confidence genes were identified in a 34.74-Mb physical interval. TraesCS1A02G045300 and TraesCS1A02G058400 were among the putative candidate genes associated with kernel traits, and they were expressed during grain development. Moreover, we also developed high-throughput kompetitive allele-specific PCR (KASP) markers of TaTKW-1A, validated in a natural population of 114 wheat varieties. The study provides a basis for cloning the functional genes underlying the QTL for kernel traits and a practical and accurate marker for molecular breeding.