Knitted textiles are a popular reinforcement in polymer composites for their high drape properties and superior impact energy absorption, making them suitable for specific composite components. Nevertheless, limited attention has been paid to modeling the mechanical behavior of knitted fabric composites since knitted textiles generally offer lower stiffness and strength. This study presents a 3D finite element (FE) modeling of a precise geometrical model of weft-knitted carbon fiber thermoplastic composite to better understand its nonlinear mechanical behavior and interface damage mechanisms under tension. Toward this end, a representative volume element (RVE) of the weft-knitted fabric composite with periodic boundary conditions (PBCs) is generated based on actual dimensions. The validity of the textile RVE to represent the macroscopic behavior was evaluated prior to analyzing the composite. The effect of fiber tow/matrix debonding during tension on the mechanical behavior of the composite is investigated using the cohesive zone model (CZM). Finally, the predicted results of the mechanical behavior of the composite with and without considering the interface failure are compared with the experimental measurements. It is found that the fiber tow/matrix interfacial strength has a significant effect on the tensile performance of the knitted fabric composites, particularly when they are subjected to a large strain. According to the simulation results, the highest tensile performance of the composite is achieved when the interfacial debonding is prevented. However, considering the fiber/matrix debonding in the modeling is essential to achieve a good agreement with the experimental results. In addition, it is concluded that stretching the fabric before composite manufacturing can substantially increase the tensile stiffness of the knitted composite.