In this paper, we propose a path planning method for the localization of radiation sources using a mobile robot equipped with an imaging gamma-ray detector, which has a field of view in all directions. The ability to detect and localize radiation sources is essential for ensuring nuclear safety, security, and surveillance. To enable the autonomous localization of radiation sources, the robot must have the ability to automatically determine the next location for gamma ray measurement instead of following a predefined path. The number of incident events is approximated to be the squared inverse proportional to the distance between the radiation source and the detector. Therefore, the closer the distance to the source, the shorter the time required to obtain the same radiation counts measured by the detector. Hence, the proposed method is designed to reduce this distance to a position where a sufficient number of gamma-ray events can be obtained; then, a path to surround the radiation sources is generated. The proposed method generates this path by performing principal component analysis based on the results obtained from previous measurements. Both simulations and actual experiments demonstrate that the proposed method can automatically generate a measurement path and accurately localize radiation sources.