Amyloid-beta peptides are known to form amyloid fibrils and are considered to play an important role in Alzheimer's disease. Amyloid-beta(29-42) is a fragment of the amyloid-beta peptide and also has a tendency to form amyloid fibrils. In order to study the mechanism of amyloidogenesis of this fragment, we applied one of the generalized-ensemble algorithms, the multicanonical-multioverlap algorithm, to amyloid-beta(29-42) dimer in aqueous solution. We obtained a detailed free-energy landscape of the dimer system. From the detailed free-energy landscape, we examined monomer and dimer formations of amyloid-beta(29-42) and deduced dimerization processes, which correspond to seeding processes in the amyloidogenesis of amyloid-beta(29-42).