Quantum confinement in semiconductor nanowires is of contemporary interest. Enhancing the quantum efficiency of quantum wells in nanowires and minimizing intrinsic absorption are necessary for reducing the threshold of nanowire lasers and are promising for wavelength tunable emitters and detectors. Here, we report on growth and optimization of GaAs1-xSbx/Al1-yGayAs quantum well heterostructures formed radially around pure zinc blende GaAs core nanowires. The emitted photon energy from GaAs0.89Sb0.11 quantum well (1.371 eV) is smaller than the GaAs core, thus showing advantages over GaAs/Al1-yGayAs quantum well nanowires in photon emission. The high optical quality quantum well (internal quantum efficiency reaches as high as 90%) is carefully positioned so that the quantum well coincides with the maximum of the transverse electric (TE01) mode intensity profile. The obtained superior optical performance combined with the supported Fabry-Perot (F-P) cavity in the nanowire leads to the strong amplified spontaneous emission (ASE). Detailed studies of the amplified cavity mode are carried out by spatial-spectral photoluminescence (PL) imaging, where emission from nanowire is resolved both spatially and spectrally. Resonant emission is generated at nanowire ends and is polarized perpendicular to the nanowire, in agreement with the simulated polarization characteristics of the TE01 mode in the nanowire. The observation of strong ASE for single QW nanowire at room temperature shows the potential application of GaAs1-xSbx QW nanowires as low threshold infrared nanowire lasers.