Aiming at the problem of high cross polarization level of traditional rectangular waveguide narrow edge inclined slot antenna， a rhombic slot antenna at ridge edge of single ridge waveguide with high radiation efficiency is designed in this paper. The effects of the ratio of waveguide narrow side to the wide side， the ratio of ridge depth to the waveguide narrow side， the ratio of ridge edge width to waveguide wide side， and the width side of the waveguide on the slot resonance are studied by the method of theoretical analysis and electromagnetic simulation. The results show that when the ratio of the narrow side to the wide side of the waveguide and the ratio of the ridge depth to the narrow side of the waveguide changes， the resonant cutting depth change in the opposite direction， and the resonance conductance change in the same direction； when the ratio of the wide side of the waveguide changes， the resonant cutting depth and the resonant conductance change in the opposite direction； when the ratio of the ridge edge width to the wide side of the waveguide changes， the resonant cutting depth and the resonant conductance change in the same direction. According to the influence law of waveguide geometric parameters on slot resonance， the optimal waveguide geometric parameters are selected， and a 16 element single ridge waveguide ridge edge slot array is designed. The slot is arranged in rhombic shape to reduce the cross polarization level. The gain is 18.02 dB， the side lobe level is lower than -19.64 dB， and the cross polarization level is lower than -46.51 dB. Compared with the traditional rectangular waveguide narrow edge slot antenna， the antenna has the advantages of light weight， low cross polarization level.