We introduce quiver gauge theory associated with the non-simply laced type fractional quiver and define fractional quiver W-algebras by using construction of Kimura and Pestun (Lett Math Phys, 2018. https://doi.org/10.1007/s11005-018-1072-1; Lett Math Phys, 2018. https://doi.org/10.1007/s11005-018-1073-0) with representation of fractional quivers.