To solve the problem that how to design a big magnetic moment, small size, light weight, low power consumption magnetorquer with air core under the constraint of limited volume and power in CubSate, multiobjective optimization design method is used. Firstly, based on the structure of the square support with multiple layer of the enameled wire wrapped, the magnetic moment model, power consumption model and mass model are deduced from square support size, enameled wire diameter and turn number, respectively. Secondly, according to the model of magnetic moment and power consumption, the multi-objective optimization design of magnetorquer with genetic algorithm (GA) is used under the constraint of limited mass and volume. Thirdly, based on the relation between the magnetic moment and the magnetic induction intensity, the measurement method of the magnetic moment is designed. Finally, the designed parameter is implemented. The test result showed that the designed magnetorquer has the qualities of high linearity, low remanence, and it well met the requirements of CubeSat standard. The designed magnetorquer successfully applied in several CubeSats indicates the reliability of this design scheme.