Grain weight and grain number are important yield component traits in wheat and identification of the underlying genetic loci is helpful for improving yield. Here we identified eight stable quantitative trait loci (QTL) for yield component traits, including five loci for thousand grain weight (TGW) and three for grain number per spike (GNS) in a recombinant inbred line population derived from the cross of Yangxiaomai and Zhongyou 9507 across four environments. Since grain size is a major determinant of grain weight, we mapped QTLs for grain length (GL) and grain width (GW). Four TGW QTLs, QTGW.caas-2D, QTGW.caas-3B, QTGW.caas-5A and QTGW.caas-7A.2 co-located with those for grain size. QTGW.caas-2D also had a consistent genetic position with QGNS.caas-2D, suggesting that the pleiotropic locus is a modulator of trade-off effect between TGW and GNS. Sequencing and linkage mapping showed that TaGL3-5A and WAPO-A1 were candidate genes of QTGW.caas-5A and QTGW.caas-7A.2, respectively. We developed kompetitive allele specific PCR (KASP) markers linked with the stable QTLs for yield component traits and validated their genetic effects in a diverse panel of wheat cultivars from the Yellow-Huai River Valley region. KASP-based genotyping analysis further revealed that the superior alleles of all stable QTLs for TGW but not GNS were subject to positive selection, indicating that yield improvement in the region largely depends on increased TGW. Comparative analyses with previous studies showed that most of the QTLs could be detected in different genetic backgrounds, and QTGW.caas-7A.1 is likely a new QTL. These findings provide not only valuable genetic information for yield improvement but also useful tools for marker-assisted selection.