Interactions of amyloid-β (Aβ) with neuronal membrane are associated with the progression of Alzheimer's disease (AD). Ganglioside GM1 has been shown to promote the structural conversion of Aβ and increase the rate of peptide aggregation; but the exact nature of interaction driving theses processes remains to be explored. In this work, we have carried out atomistic-scale computer simulations (totaling 2.65 µs) to investigate the behavior of Aβ monomer and dimers in GM1-containing raft-like membrane. The oligosaccharide head-group of GM1 was observed to act as scaffold for Aβ-binding through sugar-specific interactions. Starting from the initial helical peptide conformation, a β-hairpin motif was formed at the C-terminus of the GM1-bound Aβ-monomer; that didn't appear in absence of GM1 (both in fluid POPC and liquid-ordered cholesterol/POPC bilayers and also in aqueous medium) within the simulation time span. For Aβ-dimers, the β-structure was further enhanced by peptide-peptide interactions, which might influence the propensity of Aβ to aggregate into higher-ordered structures. The salt-bridges and inter-peptide hydrogen bonds were found to account for dimer stability. We observed spontaneous formation of intra-peptide D(23)-K(28) salt-bridge and a turn at V(24)GSN(27) region - long been accepted as characteristic structural-motifs for amyloid self-assembly. Altogether, our results provide atomistic details of Aβ-GM1 and Aβ-Aβ interactions and demonstrate their importance in the early-stages of GM1-mediated Aβ-oligomerisation on membrane surface.