Grain protein content (GPC) is one of the most important criteria to determine the quality of common wheat (Triticum aestivum). One of the major obstacles for bread wheat production is the negative correlation between GPC and grain yield (GY). Previous studies demonstrated that the deviation from this inverse relationship is highly heritable. However, little is known about the genetics controlling these deviations in common wheat. To fill this gap, we performed quantitative trait locus (QTL) analysis for GY, GPC, and four derived GY-GPC indices using an eight-way multiparent advanced generation intercross population comprising 394 lines. Interval mapping was conducted using phenotypic data from up to nine environments and genotypic data from a 20k single-nucleotide polymorphism array. The four indices were highly heritable (0.76-0.88) and showed distinct correlations to GY and GPC. Interval mapping revealed that GY, GPC, and GY-GPC indices were controlled by 6, 12, and 12 unique QTL, of which each explained only a small amount of phenotypic variance (R2 ≤ 10%). Ten of the 12 index QTL were independent of loci affecting GY and GPC. QTL regions harboured several candidate genes, including Rht-1, WAPO-A1, TaTEF-7A, and NRT2.6-7A. The study confirmed the usefulness of indices to mitigate the inverse GY-GPC relationship in breeding, though the selection method should reflect their polygenic inheritance.