The work was conducted to determine the practical applicability of size-exclusion high performance liquid chromatography in testing wheat bread-making quality and specify which of the peak characteristics, is the best indicator of wheat quality. The research was realized on 29 cultivars of different quality. The wheat quality was evaluated by protein content, content of wet gluten, gluten index, and farinograph rheological characteristics. All of the determined peak characteristics can be used as the indicators of wheat quality but the closest correlations with the quality parameters were found for the absolute peak areas and/or relative peak areas. The area of peak 1 was positively correlated with the dough stability (r = 0.50) and negatively correlated with the degree of dough softening (r = −0.49). The relative and absolute areas of the peak 2 were in positive correlation with sedimentation volume (r = 0.68; 0.68), farinograph water absorption (r = 0.50; 0.57) and protein content (r = 0.56; 0.57). The characteristics of peaks 3 and 4 were in the closest correlation with the investigated parameters of bread-making quality, the correlation coefficients related to the peaks 3 and 4 were nearly equal and reached values 0.58–0.77. The peak height can be used as a supplemental wheat quality indicator especially for determination of certain glutenin subunits. The area/height ratio or the contents of protein fractions are of the minor importance. Then the model predicting bread-making quality from peak characteristics was built. The values of coefficients of determination R2 were the highest for Zeleny sedimentation volume (0.83–0.97). The agreement between predicted and observed values increased when not single characteristics, but their combinations were considered.