Capitalization of winery by-products has received high interest among scientists, producers and consumers concerned with healthy diet and environment protection. Grape peels are rich in fiber and polyphenols and can be used as ingredients in pasta matrix in order to increase the nutritional and functional value of such a staple food. The aim of this paper was to investigate the effects of grape peel flour added in various amounts (1–6%) to common wheat pasta dough viscoelasticity and texture and on pasta chemical composition, color, cooking behavior and texture, revealing at the same time the relations between characteristics. Grape peel flour induced the increase of the elastic (G′) and viscous (G″) moduli, dough hardness, springiness, cohesiveness, pasta crude ash, crude fat, crude fiber, total polyphenols and resistant starch contents, pasta water absorption, cooking loss and breaking force as the addition level was higher and compared to the control. On the other hand, dough resilience, pasta luminosity, chewiness and firmness decreased as the amount of grape peel flour raised. Significant correlations (p < 0.05) were obtained between the chemical composition and color parameters, while crude fiber, protein and fat were correlated with dough and pasta texture, total polyphenols with resistant starch content, cooking loss with crude fiber and dough textural parameters. The obtained results underlined the opportunity to use a valuable byproduct such as grape peels in novel pasta formulations, being helpful for processors to extend the product variety and to optimize the processes in order to better satisfy consumer’s demand for functional foods.