The amalgamation of high-strained core/shell geometries in nanowire (NW) heterostructures with bandgap engineering enables the systems with novel transport and optical properties. Herein, the lattice-mismatch-high construction GaAs/GaSb/GaAs core-dual-shell (CDS) NWs were grown by molecular beam epitaxy (MBE), with a focus on exploring the impact of strain on their bandgap characteristics. Interestingly, the high stain between GaSb and GaAs leads to the surface roughening that favors Stranski-Krastanov (SK) mode growth, and coherent GaSb islands on GaAs NWs form plastically relaxed mounds at the edges of the NW sidewall facets. Strain properties of GaAs/GaSb/GaAs CDS NWs have been investigated systematically by X-ray diffraction (XRD), high-resolution transmission electron microscopy (HRTEM), and Raman spectra. It is clearly revealed that the presence of different strains, with the strain diminished of GaSb shell layer in the large-scale NWs and amplified in the small-scale NWs. The optical properties of the GaAs/GaSb/GaAs CDS NWs were investigated by power- and temperature-dependent photoluminescence (PL) measurements, which reveal the emission properties with the exciton localization phenomenon. Our results on the unique optical properties of localized excitons in GaAs/GaSb/GaAs core-shell nanostructures open the way to the design of stable optoelectronic devices.