Grain protein content (GPC) is controlled by complex genetic systems and their interactions, and is an important quality determinant for hard spring wheat as it has a positive effect on bread and pasta quality. GPC is variable among genotypes and strongly influenced by environment. Thus, understanding the genetic control of wheat GPC and identifying genotypes with improved stability is an important breeding goal. The objectives of this research were to identify genetic backgrounds with less variation for GPC across environments and identify quantitative trait loci (QTLs) controlling the stability of GPC. A spring wheat nested association mapping (NAM) population of 650 recombinant inbred lines (RIL) derived from 26 diverse founder parents crossed to one common parent, 'Berkut', was phenotyped over three years of field trials (2014-2016). Genomic selection models were developed and compared based on prediction of GPC and GPC stability. After observing variable genetic control of GPC within the NAM population, seven RIL families displaying reduced marker-by-environment interaction were selected based on a stability index derived from Finlay-Wilkinson regression. A genome-wide association study identified seven significant QTLs for GPC stability with a Bonferroni-adjusted P value <0.05. This study also demonstrated that genome-wide prediction of GPC with ridge regression best linear unbiased estimates reached up to r = 0.69. Genomic selection can be used to apply selection pressure for GPC and improve genetic gain for GPC.