The mechanisms by which amyloidogenic peptides and proteins form soluble toxic oligomers remain elusive. We have studied the formation of partially ordered tetramers and well-ordered octamers; of an amyloidogenic hexapeptide NFGAIL (residues 22-27 of the human islet amyloid polypeptide) in our previous work. Continuing the effort, we here probe the beta-sheet elongation process by a combined total of 2.0 mu s molecular dynamics simulations with explicit solvent. In a set of 10 simulations with the peptides restrained to the extended conformation, we observed that the main growth mode was elongation along the beta-sheet hydrogen bonds through primarily a two-stage process. Driven by hydrophobic forces, the peptides initially attached to the surface of the ordered oligomer, moved quickly to the beta-sheet edges, and formed stable beta-sheet hydrogen bonds. Addition of peptides to the existing oligomer notably improved the order of the peptide aggregate in which labile outer layer beta-sheets were stabilized, which provides good templates for further elongation. These simulations suggested that elongation along the beta-sheet hydrogen bonds occurs at the intermediate stage when low-weight oligomers start to form. We did not observe significant preference toward either parallel or antiparallel beta-sheets at the elongation stage for this peptide. In another set of 10 unrestrained simulations, the dominant growth mode was disordered aggregation. Taken together, these results offered a glimpse at the molecular events leading to the formation of ordered and disordered low-weight oligomers.