Formation of fibrillar fibronectin networks is a major process during embryogenesis and tissue formation, but the molecular details of fibril assembly remain poorly understood. Based on current ideas of fibronectin fibrillogenesis, a stochastic model was developed to enlighten the mechanism of the formation of paired fibronectin nanofibrils by adherent endothelial cells, which has been observed recently. The development of fibronectin clusters and fibrils was investigated by means of Monte Carlo simulations, including diffusion-controlled aggregation and myosin-driven transport of fibronectin-integrin complexes in the vicinity of a focal adhesion. Different evolving growth patterns were summarized in a morphological diagram as a function of the fibronectin substrate and fibronectin-fibronectin interaction energies. The formation of paired nanofibrils was found to occur in a certain region of interaction parameters. Beyond this region branched fibronectin clusters as well as tear-off of fibronectin fibrils were observed.