Gold nanoparticle (AuNP) assemblies in two-dimensions (2D) exhibit collective physical/chemical properties that are useful for various devices. However, technical issues still impede the efficient ordering of differently sized AuNPs on solid supports while avoiding phase separation. This paper describes a method to construct binary 2D assemblies by folding precursory circular chains composed of small and large AuNPs. The structural change is caused by a spontaneous, non-cross-linking assembly of fully matched double-stranded DNA-modified AuNPs (dsDNA-AuNPs) at a high ionic strength. Since larger dsDNA-AuNPs have a lower critical coagulation concentration of the supporting electrolyte, the spontaneous assembly of large AuNPs precedes that of small AuNPs in the precursory chain during evaporation. Transmission electron microscopy reveals that alternate-type AuNP chains are folded into a binary 2D structure in a mixed mode, whereas block-type chains are transformed into a binary 2D structure in a core-shell mode. The methodology could potentially be harnessed for the fabrication of binary AuNP arrays for various devices.