This paper describes the characteristics of a one dimensional narrow-wall slotted waveguide array with a single-layer linear-to-circular polarization converter consisting of a dipole array. An external boundary value Problem of one slot and three dipoles, which approximates the mutual coupling between the dipole array and an edge slot extending over three faces of a rectangular waveguide, is formulated and analyzed by the method of moments; design of polarization conversion is conducted for this model as a unit element. If every unit element has perfect circular polarization, grating lobes appear in the array pattern due to the alternating slot angle: these are suppressed in this paper by changing the dipole angle and degrading the axial ratio of the unit element. The validity of the design is confirmed by the measurements. The dipole array has negligible effects upon slot impedance; the polarization conversion for existing narrow-wall slotted arrays is realized by add-on dipole array.