For dedicated brain PET, we can significantly improve sensitivity for the cerebrum region by arranging detectors in a compact hemisphere. The geometrical sensitivity for the top region of the hemisphere is increased compared with conventional cylindrical PET consisting of the same number of detectors. However, the geometrical sensitivity at the center region of the hemisphere is still low because the bottom edge of the field-of-view is open, the same as for the cylindrical PET. In this paper, we proposed a helmet PET with add-on detectors for high sensitivity brain PET imaging for both center and top regions. The key point is the add-on detectors covering some portion of the spherical surface in addition to the hemisphere. As the location of the add-on detectors, we proposed three choices: a chin detector, ear detectors, and a neck detector. For example, the geometrical sensitivity for the region-of-interest at the center was increased by 200% by adding the chin detector which increased the size by 12% of the size of the hemisphere detector. The other add-on detectors gave almost the same increased sensitivity effect as the chin detector did. Compared with standard whole-body-cylindrical PET, the proposed geometries can achieve 2.6 times higher sensitivity for brain region even with less than 1/4 detectors. In addition, we conducted imaging simulations for geometries with a diameter of 250 mm and with high resolution depth-of-interaction detectors. The simulation results showed that the proposed geometries increased image quality, and all of the add-on detectors were equivalently effective. In conclusion, the proposed geometries have high potential for widespread applications in high-sensitivity, high-resolution, and low-cost brain PET imaging.