The composite material textile reinforced concrete (TRC) requires a high bond performance between the fiber strand and the concrete matrix. While the influence of the textile on bond behavior is well known, in this publication the influence of the concrete matrix is investigated by means of single-sided pull-out tests. The results of the presented study show dependence between the concrete strength and bond performance of the composite material. When a concrete of a higher-strength class is used, the bond-flow–pull-out distance curve shifts upward independent of the textile geometry and the yarn impregnation. A simplified model is presented to predict the occurrence of a crack along the fiber strand. This model serves as a basis to investigate the correlation between concrete width per fiber strand and resistance against a splitting crack. The effective concrete tensile strength decreases to about 35% when the concrete width is increased from 10 mm to 50 mm. To quantify the decrease, a mathematical relationship, which describes the test results independent of textile and concrete type, is proposed.