Use of the systematic process of design optimization was proposed using the sequential approximation technique for the 10 MeV cyclotron magnet, which is a positron emission tomography cyclotron for producing radioactive isotopes. To design cyclotrons with the conventional routine approach, too much time and an iterative process are required, because even a very small change in the magnet shape is directly linked to success or failure, as verified using the beam orbit and energy level. To resolve this sensitive and tricky problem, designers need a systematic numerical approach for developing a new design. Until now, however, related research articles have not been seen in the literature. To build a systematic optimization process for the cyclotron magnet, we adopted the Latin hypercube sampling method, one of the design of experiments, and generated sampling data. On the basis of these data, an approximation model was modeled using the Kriging technique. To find the optimal shape, an iterative searching technique was implemented, which incorporates the approximation model, restricted evolution strategy, and boundary shifting technique. The initial magnet model was obtained from the conventional routine procedure for a cyclotron. To verify our proposed model, the final magnet model was tested with a beam simulation for checking the trajectory of 18F at a level of 10 MeV at the extraction point.