A corrugated horn antenna with sparse ripple structure is proposed. The antenna with only 2 ripples is simple in structure and easy to design and process. By optimizing the parameters of the antenna, a wide beam forming of ±40° and a gain above 5 dBi can be realized. The side-lobe levels are lower than -20 dB and the Voltage Standing Wave Ratio(VSWR) is lower than 1.8. It is suitable for inter satellite communication of high orbit satellites. Through the processing, testing and comparison between measured and predicted radiation patterns of a Ka-band sample, the correctness of the design is verified.