Developing efficient, robust methods for predicting the progressive failure of carbon fiber composites under tension is essential for optimal design, balancing weight reduction, damage tolerance, and service life. Implicit finite element (FE) methods struggle with the complex interplay of failure mechanisms, leading to a heavy reliance on costly, time-consuming experimental testing. This study introduces a novel explicit algorithm designed for laminate-level mesh models, capable of simulating cohesive cracks without predefined paths. Utilizing an explicit finite element software approach, our method effectively addresses convergence issues associated with the non-linear and unstable nature of composite failures during quasi-static loading. Contrasting with implicit FE method, this mesh-independent approach is both practical and numerically robust. The algorithm’s performance, tested on carbon-fiber reinforced composites with varying ply configurations [452/-452]s, [45n/90n/-45n/0n]s and [45/90/-45/0]ns (n=1/2/4/8), demonstrates improved simulation accuracy and efficiency over implicit FE methods, aligning well with prior experimental and simulation data. This advancement offers a promising solution for accurately simulating and understanding the complex failure behavior of these composites.