The aim of the research was the development of an alternative formula for gluten-free bread (GFB) containing amaranth flour. GFBs were prepared using a 23 factorial screening experimental design. The amount of water, albumen and fat varied in order to evaluate their impact on the textural, structural and sensory characteristics of the final product. Water amount had the greatest influence on bread characteristics. For a 33% water content increase (from 0.6 to 0.8 g g−1 of flour) the firmness of the crumb decreased to 20% of the initial value. Also, for the same water content increase, the average pore size became 2.5-fold greater. Albumen addition (from 0 to 0.04 g g−1 of flour) influenced mainly crumb viscoelasticity (20% increase). Variations in fat amount did not significantly influence any of the response variables investigated. However, the combined addition of fat and albumen resulted in breads that received the best rankings in overall acceptance in sensory evaluation.