Damage and failure of the fiber reinforced composites remain as a challenging research subject in the area of material science and engineering. In this study a novel particle assembly model is developed using two dimensional Discrete Element Method (DEM) for the purpose of simulating the damage and failure process of the single-fiber composite (SFC) under axial tension. Fiber (SiC) and matrix (Epoxy) are represented by particles bonded together through elastic parallel bonds which are calibrated by a series of numerical tests. The contacts between the fiber particles and matrix particles are directly accounted for the fiber/matrix interface which is represented by the contact softening model similar to the cohesive zone model (CZM) in the continuum mechanics. The single-fiber composite tensile test is carried out using the developed DEM model in order to evaluate the interactions between fiber breakage, interfacial debonding and matrix cracking. The numerical results have demonstrated the capability of the developed DEM model in simulating the entire failure process of each individual constituent of the single fiber composite. This study has also confirmed that the DEM model has unique advantages over the conventionally numerical models in terms of dealing with the evolution of microscopic damages in composite materials.