The understanding of meso-scale fracture behavior of fiber-reinforced composite materials (such as initiation, coalescence and accumulation of microscopic damage) is important for evaluating the macroscopic strength or toughness. Thus the present study proposes a micromechanics-based simulation for the fracture of composite materials with cohesive/volumetric finite-element schemes. The present simulation handles the multiple, interacting damage mechanisms involved in the damage process of composites, including interacting fiber breaks, matrix plasticity and cracking, and interfacial debonding. First the modeling for the microscopic damage is validated and calibrated by simulating the microscopic damage in single-fiber composite (SFC) tests. The present simulation well reproduces the microscopic damage and fragmentation process in SFC tests. Based on the calibrated micromechanical model, we simulate the meso-scale fracture of short-fiber reinforced polymer-matrix composites, and discuss the effect of constitutive structure of composites on damage initiation and coalescence.