Grain yield and grain protein concentration are often negatively associated in wheat (Triticum aestivum L.). When grain yield increases and grain protein concentration decreases, the milling and baking quality of bread flour can be affected. In the Pacific Northwest region of the USA, grain yield of wheat is usually high and grain protein concentration is low. Parents, F-4 and F-5 generations of two crosses were solid-planted in two environmentally diverse but high-yielding sites in Oregon to study the association of grain protein concentration with grain yield and biological yield, harvest index and related traits in the Pacific Northwest's environment, and to suggest a selection criterion to increase grain yield while maintaining or increasing grain protein concentration. Correlation coefficients showed moderate negative associations between grain protein concentration and grain yield, and also between grain protein concentration and harvest index. Genetic correlations were larger than phenotypic correlations, while environmental correlations were low, suggesting the presence of negative genetic relationships between grain protein concentration with grain yield and with harvest index. Grain yield and harvest index were the most important traits affecting grain protein concentration as estimated by path coefficients analyses. We suggest that selection for high grain yield, while maintaining or increasing grain protein concentration, should not be based on further increases of harvest index, but rather on increasing biological yield.