To meet the requirement of multiple tasks in parallel in spaceborne communication, this paper proposes a common aperture multi-beam reflector antenna composed of a Gregorian reflector and three feed-horn antennas, which can generate two contoured beams and one spot beam. The antenna is designed using ray tracing method to determine the optimal spot beam feed position for establishing the antenna infrastructure, and employing Zernike polynomials and cubic B-splines function to optimize the shape of both the main and secondary reflectors. To validate the efficacy of the method, simulation experiments were conducted on 1.1 m diameter antenna. The results demonstrate that the edge of coverage gain for both shaped contour beams in Ku receiving and transmitting bands are 27.7 dBi, 28.0 dBi, 28.0 dBi and 28.2 dBi, respectively. The spot beam exhibits a minimum service EOC gain of not less than 34 dBi, while the scanning beam gain within the range of 0 to 6.5° is not less than 35 dBi.