A turbine nozzle having a non-linear cooling conduit is disclosed. In one embodiment, a turbine nozzle includes: an airfoil, at least one endwall adjacent the airfoil, and a fillet region connecting the airfoil and the at least one endwall, the fillet region including an outer surface. The turbine nozzle also includes a non-linear cooling conduit located within the fillet region and adjacent the outer surface of the fillet region, the non-linear cooling conduit allows fluid flow through the fillet region. The non-linear cooling conduit spans substantially along an axial length of the airfoil between a leading edge of the airfoil and a trailing edge of the airfoil. Additionally, the non-linear cooling conduit includes an arc profile substantially similar to an arc profile of the airfoil.