In recent years, the demand for gluten-free products has been constantly increasing due to the increase in the number of people suffering from celiac disease. Bread is the main product consumed in our country; therefore, gluten-free bread for celiac patients on the market is mostly of poor quality and low nutritional value, while gluten-free flour has a very high price. The purpose of this work was to investigate the rheological properties of dough, the nutritional value of bread, as well as the sensory properties of gluten-free bread produced from mixtures of raw materials such as rice, chickpea, and bean flour, corn starch, and egg powder. The results showed that the gluten-free bread had different rheological properties, and only mixes M5 and M6 had similar rheological properties, such as dough development, stability, and degree of softening, to the control bread M1. Gluten-free bread from mixtures M2 and M3 had higher contents of protein, fat, cellulose, and minerals, while bread from mixtures M5 and M6 had medium contents. Bread M2 and M3 had acidity levels above the allowed limits which made them unusable or had a short shelf life. Sensory analyses showed that bread M5 had similar sensory properties to the control bread M1 and fell into the same quality category; also, bread from the M5 mixture has a much better taste and aroma. For consumption, we recommend using gluten-free bread from the M5 mixture, which in its composition has 80% rice flour, 7.5% chickpea flour, 5% bean flour, and 7.5% egg powder.