We propose and demonstrate a novel one-dimensional nanobeam bandedge laser constituted by self-aligned nanoisland quantum-well (QW) structures. The formation of self-aligned InGaAsP nanoislands sandwiched between two InP claddings is the result of selective removal of QW through wet-etching processes. By controlling wet-etching time, we show a good spatial and spectral overlap between the dielectric mode and the self-aligned nanoisland structures leads to the realization of nanobeam bandedge lasers with low-threshold operations and high slope efficiencies. Optical characterization results indicate a strong correlation between the size of individual nanoisland and the threshold power of our nanobeam bandedge lasers. We obtain an approximately 81% reduction in the absorbed threshold power as we optimize the size of the nanoislands.