Abstract: Geostationary-Orbit fully-flexible satellite can dynamically adjust coverage, power, frequency and other resources in orbit to meet the time-varying traffic requirements of users in different geographic regions, which is of significant importance for the future development of commercial and civil high-throughput satellite systems. As a crucial technology of achieving the flexible adjustment of coverage and power resources for the fully-flexible satellites, digital phased array-based multi-beam forming technology has become a hotspot of current research. To achieve precise shaping of various-sized spot beams and flexible adjustment of beam power resources, as well as to improve the total radiation power of the array and the carrier-to-interference ratio of the system, this paper models a multi-objective, multi-constraint optimization problem that takes into account several practical factors, such as beam pointing, width, maximum side-lobe level, power allocation ratio, and total radiation power of the array. A fast multi-beam forming algorithm for the phased array based on the genetic algorithm is proposed. Simulation results show that the proposed algorithm not only exhibits superior performance in beam shaping and beam power allocation, but also the total radiation power of the array has improved by 2.5 times compared to the traditional method, and the carrier-to-interference ratio of each beam has reached 15 dB ~ 20 dB.